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AWK, 96 86 bytes

#AWK, 96 86 bytes Subtitle: Look Mom! Only adding and some bookkeeping!

#AWK, 96 86 bytes Subtitle: Look Mom! Only adding and some bookkeeping!

AWK, 96 86 bytes

Subtitle: Look Mom! Only adding and some bookkeeping!

deleted 22 characters in body
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File x.bash (no trailing newline):

File x.bash (no trailing newline):

File x.bash:

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#AWK, 9696 86 bytes Subtitle: Look Mom! Only adding and some bookkeeping!

BEGIN{for(n=2;l<ARGV[1];n=2;l<$1;){if(n in L)p=L[n]
else{print p=n;l++}
for(N=p+n++;N in L;)N+=p
L[N]=p}}
$ awk -f fsoe3.awk <<< 5
2
3
5
7
11
$ awk -f fsoe3.awk <<< 1000 | wc -l
1000

#AWK, 96 bytes Subtitle: Look Mom! Only adding and some bookkeeping!

BEGIN{for(n=2;l<ARGV[1];){if(n in L)p=L[n]
else{print p=n;l++}
for(N=p+n++;N in L;)N+=p
L[N]=p}}
$ awk -f fsoe3.awk 5
2
3
5
7
11
$ awk -f fsoe3.awk 1000 | wc -l
1000

#AWK, 96 86 bytes Subtitle: Look Mom! Only adding and some bookkeeping!

{for(n=2;l<$1;){if(n in L)p=L[n]
else{print p=n;l++}
for(N=p+n++;N in L;)N+=p
L[N]=p}}
$ awk -f fsoe3.awk <<< 5
2
3
5
7
11
$ awk -f fsoe3.awk <<< 1000 | wc -l
1000
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