A349182 a(0) = 1; for n>0, a(n) is the smallest positive integer such that |n - a(n-1)| + a(n) is a square.

1, 1, 3, 1, 1, 5, 3, 5, 1, 1, 7, 5, 2, 5, 7, 1, 1, 9, 7, 4, 9, 4, 7, 9, 1, 1, 11, 9, 6, 2, 8, 2, 6, 9, 11, 1, 1, 13, 11, 8, 4, 12, 6, 12, 4, 8, 11, 13, 1, 1, 15, 13, 10, 6, 1, 10, 3, 10, 1, 6, 10, 13, 15, 1, 1, 17, 15, 12, 8, 3, 14, 7, 16, 7, 14, 3, 8, 12, 15, 17, 1, 1, 19, 17, 14, 10, 5, 18, 11

Offset: 0

Author

Scott R. Shannon, Nov 09 2021

Keywords

• nonn

Examples

			a(1) = 1 as |1 - a(0)| = |1 - 1| = 0, and 0 + 1 = 1 = 1^2 is the next smallest square.
a(2) = 3 as |2 - a(1)| = |2 - 1| = 1, and 1 + 3 = 4 = 2^2 is the next smallest square.
a(5) = 5 as |5 - a(4)| = |5 - 1| = 4, and 4 + 5 = 9 = 3^2 is the next smallest square.
		

Links

• Scott R. Shannon, Image for the first 50000 terms.

Crossrefs

Cf. A349119, A000290, A347595, A347594, A009000, A347754.

Programs

Mathematica

nxt[{n_,a_}]:={n+1,Module[{k=1},While[!IntegerQ[Sqrt[(Abs[n+1-a])+k]],k++];k]}; NestList[ nxt,{0,1},90][[;;,2]] (* Harvey P. Dale, Aug 20 2024 *)