3 minor update

# JavaScript (ES6), 165 bytes

Prints the indices with alert().

f=(n,x=w=y=n+2)=>y+w&&[0,-1,0,1].map((d,i)=>(g=(x,y,A=Math.abs)=>(k=A(A(x)-A(y))+A(x)+A(y))*k+(k+x+y)*(y>=x||-1))(x+d,y+~-i%2)-n||alert(g(x,y)))|f(n,x+w?x-1:(y--,w))


Try it online!

### How?

This is based onFor $$\x, y \in \mathbb{Z}\$$, we compute the following formula0-based index $$\I_{x,y}\$$ of the spiral with:

$$A_{x,y}=||x|-|y||+|x|+|y|$$ $$S_{x,y}=\begin{cases}1,&\text{if }y\ge x\\-1,&\text{if }y $$I_{x,y}=A_{x,y}^2+(A_{x,y}+x+y)\times S_{x,y}$$

# JavaScript (ES6), 165 bytes

Prints the indices with alert().

f=(n,x=w=y=n+2)=>y+w&&[0,-1,0,1].map((d,i)=>(g=(x,y,A=Math.abs)=>(k=A(A(x)-A(y))+A(x)+A(y))*k+(k+x+y)*(y>=x||-1))(x+d,y+~-i%2)-n||alert(g(x,y)))|f(n,x+w?x-1:(y--,w))


Try it online!

### How?

This is based on the following formula:

$$A_{x,y}=||x|-|y||+|x|+|y|$$ $$S_{x,y}=\begin{cases}1,&\text{if }y\ge x\\-1,&\text{if }y $$I_{x,y}=A_{x,y}^2+(A_{x,y}+x+y)\times S_{x,y}$$

# JavaScript (ES6), 165 bytes

Prints the indices with alert().

f=(n,x=w=y=n+2)=>y+w&&[0,-1,0,1].map((d,i)=>(g=(x,y,A=Math.abs)=>(k=A(A(x)-A(y))+A(x)+A(y))*k+(k+x+y)*(y>=x||-1))(x+d,y+~-i%2)-n||alert(g(x,y)))|f(n,x+w?x-1:(y--,w))


Try it online!

### How?

For $$\x, y \in \mathbb{Z}\$$, we compute the 0-based index $$\I_{x,y}\$$ of the spiral with:

$$A_{x,y}=||x|-|y||+|x|+|y|$$ $$S_{x,y}=\begin{cases}1,&\text{if }y\ge x\\-1,&\text{if }y $$I_{x,y}=A_{x,y}^2+(A_{x,y}+x+y)\times S_{x,y}$$

# JavaScript (ES6), 165 bytes

Prints the indices with alert().

f=(n,x=w=y=n+2)=>y+w&&[0,-1,0,1].map((d,i)=>(g=(x,y,A=Math.abs)=>(k=A(A(x)-A(y))+A(x)+A(y))*k+(k+x+y)*(y>=x||-1))(x+d,y+~-i%2)-n||alert(g(x,y)))|f(n,x+w?x-1:(y--,w))


Try it online!

### How?

This is based on the following formula:

$$A_{x,y}=||x|-|y||+|x|+|y|$$ $$S_{x,y}=\begin{cases}1,&\text{if }y\ge x\\-1,&\text{if }y $$I_{x,y}=A_{x,y}^2+(A_{x,y}+x+y)\times S_{x,y}$$

# JavaScript (ES6), 165 bytes

Prints the indices with alert().

f=(n,x=w=y=n+2)=>y+w&&[0,-1,0,1].map((d,i)=>(g=(x,y,A=Math.abs)=>(k=A(A(x)-A(y))+A(x)+A(y))*k+(k+x+y)*(y>=x||-1))(x+d,y+~-i%2)-n||alert(g(x,y)))|f(n,x+w?x-1:(y--,w))


Try it online!

# JavaScript (ES6), 165 bytes

Prints the indices with alert().

f=(n,x=w=y=n+2)=>y+w&&[0,-1,0,1].map((d,i)=>(g=(x,y,A=Math.abs)=>(k=A(A(x)-A(y))+A(x)+A(y))*k+(k+x+y)*(y>=x||-1))(x+d,y+~-i%2)-n||alert(g(x,y)))|f(n,x+w?x-1:(y--,w))


Try it online!

### How?

This is based on the following formula:

$$A_{x,y}=||x|-|y||+|x|+|y|$$ $$S_{x,y}=\begin{cases}1,&\text{if }y\ge x\\-1,&\text{if }y $$I_{x,y}=A_{x,y}^2+(A_{x,y}+x+y)\times S_{x,y}$$

Prints the indices with alert().
f=(n,x=w=y=n+2)=>y+w&&[0,-1,0,1].map((d,i)=>(g=(x,y,A=Math.abs)=>(k=A(A(x)-A(y))+A(x)+A(y))*k+(k+x+y)*(y>=x||-1))(x+d,y+~-i%2)-n||alert(g(x,y)))|f(n,x+w?x-1:(y--,w))