5 deleted 2 characters in body
Ans→N:While X<N:IS>(A,A::A:prgmA:Ans→B:A²:prgmA:If B=Ans:IS>(X,N:End:A ;prgmCDGF1E

Ans→N            ;store the input in N
While X<N        ;loop until the Nth term has been reached
; (Increment A and skip the next statement if A>A)
A                ;leave A in Ans
prgmA            ;call the helper program below
Ans→B            ;store the result of the helper program in B
A²               ;square A and leave the result in Ans
prgmA            ;call the helper program below
; (result is in Ans)
If B=Ans         ;if the two results are equal
; (Increment X and skip the next statement if X>N)
End
A                ;leave A in Ans
;implicit print of Ans

sum(int(10fPart(Ans₁₀^(seq(⁻X-1,X,0,log(Ans    ;prgmA

seq(⁻X-1,X,0,log(Ans    ;generate a list...
; using X as the variable,
; starting at 0,
; ending at the log of Ans,
; and evaluating "⁻X-1" for each element
; (implicit increment of 1)
₁₀^(                        ;raise 10 to the power of each element
Ans                           ;multiply each element by the input
fPart(                              ;remove the integer part from each element
10                                    ;multiply each element by 10
int(                                      ;round each element to the nearest integer
sum(                                          ;then sum the resulting list

Ans→N:While X<N:IS>(A,A::A:prgmA:Ans→B:A²:prgmA:If B=Ans:IS>(X,N:End:A ;prgmCDGF1E

Ans→N            ;store the input in N
While X<N        ;loop until the Nth term has been reached
; (Increment A and skip the next statement if A>A)
A                ;leave A in Ans
prgmA            ;call the helper program below
Ans→B            ;store the result of the helper program in B
A²               ;square A and leave the result in Ans
prgmA            ;call the helper program below
; (result is in Ans)
If B=Ans         ;if the two results are equal
; (Increment X and skip the next statement if X>N)
End
A                ;leave A in Ans
;implicit print of Ans

sum(int(10fPart(Ans₁₀^(seq(⁻X-1,X,0,log(Ans    ;prgmA

seq(⁻X-1,X,0,log(Ans    ;generate a list...
; using X as the variable,
; starting at 0,
; ending at the log of Ans,
; and evaluating "⁻X-1" for each element
; (implicit increment of 1)
₁₀^(                        ;raise 10 to the power of each element
Ans                           ;multiply each element by the input
fPart(                              ;remove the integer part from each element
10                                    ;multiply each element by 10
int(                                      ;round each element to the nearest integer
sum(                                          ;then sum the resulting list

Ans→N:While X<N:IS>(A,A::A:prgmA:Ans→B:A²:prgmA:If B=Ans:IS>(X,N:End:A ;prgmCDGF1E

Ans→N            ;store the input in N
While X<N        ;loop until the Nth term has been reached
; (Increment A and skip the next statement if A>A)
A                ;leave A in Ans
prgmA            ;call the helper program below
Ans→B            ;store the result of the helper program in B
A²               ;square A and leave the result in Ans
prgmA            ;call the helper program below
; (result is in Ans)
If B=Ans         ;if the two results are equal
; (Increment X and skip the next statement if X>N)
End
A                ;leave A in Ans
;implicit print of Ans

sum(int(10fPart(Ans₁₀^(seq(⁻X-1,X,0,log(Ans   ;prgmA

seq(⁻X-1,X,0,log(Ans    ;generate a list...
; using X as the variable,
; starting at 0,
; ending at the log of Ans,
; and evaluating "⁻X-1" for each element
; (implicit increment of 1)
₁₀^(                       ;raise 10 to the power of each element
Ans                           ;multiply each element by the input
fPart(                              ;remove the integer part from each element
10                                    ;multiply each element by 10
int(                                      ;round each element to the nearest integer
sum(                                          ;then sum the resulting list

4 Golfed the code. Reduced byte count by 4.

# TI-BASIC 47 + 19 = 6666 62 bytes

Ans→N:While X<N:IS>(A,A::A:prgmA:Ans→B:A²:prgmA:Ans→C:If B=CB=Ans:IS>(X,N:End:A
sum(int(10fPart(Ans₁₀^(seq(⁻X-1,X,0,log(Ans

Ans→N:While X<N:IS>(A,A::A:prgmA:Ans→B:A²:prgmA:Ans→C:If B=CB=Ans:IS>(X,N:End:A ;prgmCDGF1E

Ans→N            ;store the input in N
While X<N        ;loop until the Nth term has been reached
; (Increment A and skip the next statement if A>A)
A                ;leave A in Ans
prgmA            ;call the helper program below
Ans→B            ;store the result of the helper program in B
A²               ;square A and leave the result in Ans
prgmA            ;call the helper program below
Ans→C            ;store the result of the helper; program(result is in CAns)
If B=C  B=Ans         ;if the two results are equal
; (Increment X and skip the next statement if X>N)
End
A                ;leave A in Ans
;implicit print of Ans

sum(int(10fPart(Ans₁₀^(seq(⁻X-1,X,0,log(Ans    ;prgmA

seq(⁻X-1,X,0,log(Ans    ;generate a list...
; using X as the variable,
; starting at 0,
; ending at the log of Ans,
; and evaluating "⁻X-1" for each element
; (implicit increment of 1)
₁₀^(                        ;raise 10 to the power of each element
Ans                           ;multiply each element by the input
fPart(                              ;remove the integer part from each element
10                                    ;multiply each element by 10
int(                                      ;round each element to the nearest integer
sum(                                          ;then sum the resulting list


# TI-BASIC 47 + 19 = 66 bytes

Ans→N:While X<N:IS>(A,A::A:prgmA:Ans→B:A²:prgmA:Ans→C:If B=C:IS>(X,N:End:A
sum(int(10fPart(Ans₁₀^(seq(⁻X-1,X,0,log(Ans

Ans→N:While X<N:IS>(A,A::A:prgmA:Ans→B:A²:prgmA:Ans→C:If B=C:IS>(X,N:End:A ;prgmCDGF1E

Ans→N            ;store the input in N
While X<N        ;loop until the Nth term has been reached
; (Increment A and skip the next statement if A>A)
A                ;leave A in Ans
prgmA            ;call the helper program below
Ans→B            ;store the result of the helper program in B
A²               ;square A and leave the result in Ans
prgmA            ;call the helper program below
Ans→C            ;store the result of the helper program in C
If B=C           ;if the two results are equal
; (Increment X and skip the next statement if X>N)
End
A                ;leave A in Ans
;implicit print of Ans

sum(int(10fPart(Ans₁₀^(seq(⁻X-1,X,0,log(Ans    ;prgmA

seq(⁻X-1,X,0,log(Ans    ;generate a list...
; using X as the variable,
; starting at 0,
; ending at the log of Ans,
; and evaluating "⁻X-1" for each element
; (implicit increment of 1)
₁₀^(                        ;raise 10 to the power of each element
Ans                           ;multiply each element by the input
fPart(                              ;remove the integer part from each element
10                                    ;multiply each element by 10
int(                                      ;round each element to the nearest integer
sum(                                          ;then sum the resulting list


# TI-BASIC 66 62 bytes

Ans→N:While X<N:IS>(A,A::A:prgmA:Ans→B:A²:prgmA:If B=Ans:IS>(X,N:End:A
sum(int(10fPart(Ans₁₀^(seq(⁻X-1,X,0,log(Ans

Ans→N:While X<N:IS>(A,A::A:prgmA:Ans→B:A²:prgmA:If B=Ans:IS>(X,N:End:A ;prgmCDGF1E

Ans→N            ;store the input in N
While X<N        ;loop until the Nth term has been reached
; (Increment A and skip the next statement if A>A)
A                ;leave A in Ans
prgmA            ;call the helper program below
Ans→B            ;store the result of the helper program in B
A²               ;square A and leave the result in Ans
prgmA            ;call the helper program below
; (result is in Ans)
If B=Ans         ;if the two results are equal
; (Increment X and skip the next statement if X>N)
End
A                ;leave A in Ans
;implicit print of Ans

sum(int(10fPart(Ans₁₀^(seq(⁻X-1,X,0,log(Ans    ;prgmA

seq(⁻X-1,X,0,log(Ans    ;generate a list...
; using X as the variable,
; starting at 0,
; ending at the log of Ans,
; and evaluating "⁻X-1" for each element
; (implicit increment of 1)
₁₀^(                        ;raise 10 to the power of each element
Ans                           ;multiply each element by the input
fPart(                              ;remove the integer part from each element
10                                    ;multiply each element by 10
int(                                      ;round each element to the nearest integer
sum(                                          ;then sum the resulting list

3 Added byte count and fixed explanation.

(Byte count to be evaluated when I have time.)

Ans→N:While X<N:IS>(A,A::A:prgmA:Ans→B:A²:prgmA:Ans→C:If B=C:IS>(X,N:End:A ;prgmCDGF1E

Ans→N            ;store the input in N
While X<N        ;loop until the Nth term has been reached
; (Increment A and skip the next statement if A>A)
A                ;leave A in Ans
prgmA            ;call the helper program below
Ans→B            ;store the result of the helper program in B
A²               ;square A and leave the result in Ans
prgmA            ;call the helper program below
Ans→C            ;store the result of the helper program in C
If B=C           ;if the two results are equal
; (Increment X and skip the next statement if X>N)
End
A                ;leave A in Ans
;implicit print of Ans

sum(int(10fPart(Ans₁₀^(seq(⁻X-1,X,0,log(Ans    ;prgmA

seq(⁻X-1,X,0,log(Ans    ;generate a list...
; using X as the variable,
; starting at 0,
; ending at the log of Ans,
; and evaluating "⁻X-1" for each element
; (implicit increment of 1)
₁₀^(                        ;raise 10 to the power of each element
Ans                           ;multiply each element by the input
fPart(                              ;remove the integer part from each element
10                                    ;multiply each element by 10
int(                                      ;round each element to the nearest integer
sum(                                          ;then sum the resulting list


(Byte count to be evaluated when I have time.)

Ans→N:While X<N:IS>(A,A::A:prgmA:Ans→B:A²:prgmA:Ans→C:If B=C:IS>(X,N:End:A ;prgmCDGF1E

Ans→N            ;store the input in N
While X<N        ;loop until the Nth term has been reached
; (Increment A and skip the next statement if A>A)
A                ;leave A in Ans
prgmA            ;call the helper program below
Ans→B            ;store the result of the helper program in B
A²               ;square A and leave the result in Ans
prgmA            ;call the helper program below
Ans→C            ;store the result of the helper program in C
If B=C           ;if the two results are equal
; (Increment X and skip the next statement if X>N)
End
A                ;leave A in Ans
;implicit print of Ans

sum(int(10fPart(Ans₁₀^(seq(⁻X-1,X,0,log(Ans   ;prgmA

seq(⁻X-1,X,0,log(Ans   ;generate a list...
; using X as the variable,
; starting at 0,
; ending at the log of Ans,
; and evaluating "⁻X-1" for each element
; (implicit increment of 1)
₁₀^(                       ;raise 10 to the power of each element
Ans                           ;multiply by the input
fPart(                              ;remove the integer part
10                                    ;multiply by 10
int(                                      ;round to the nearest integer
sum(                                          ;then sum the resulting list

Ans→N:While X<N:IS>(A,A::A:prgmA:Ans→B:A²:prgmA:Ans→C:If B=C:IS>(X,N:End:A ;prgmCDGF1E

Ans→N            ;store the input in N
While X<N        ;loop until the Nth term has been reached
; (Increment A and skip the next statement if A>A)
A                ;leave A in Ans
prgmA            ;call the helper program below
Ans→B            ;store the result of the helper program in B
A²               ;square A and leave the result in Ans
prgmA            ;call the helper program below
Ans→C            ;store the result of the helper program in C
If B=C           ;if the two results are equal
; (Increment X and skip the next statement if X>N)
End
A                ;leave A in Ans
;implicit print of Ans

sum(int(10fPart(Ans₁₀^(seq(⁻X-1,X,0,log(Ans    ;prgmA

seq(⁻X-1,X,0,log(Ans    ;generate a list...
; using X as the variable,
; starting at 0,
; ending at the log of Ans,
; and evaluating "⁻X-1" for each element
; (implicit increment of 1)
₁₀^(                        ;raise 10 to the power of each element
Ans                           ;multiply each element by the input
fPart(                              ;remove the integer part from each element
10                                    ;multiply each element by 10
int(                                      ;round each element to the nearest integer
sum(                                          ;then sum the resulting list

2 Added byte count and fixed explanation.
1