A037458 a(1)=1; for n > 1, a(n) = n - a(n-floor(sqrt(n))).

1, 1, 2, 3, 3, 3, 4, 5, 6, 6, 6, 6, 7, 8, 9, 10, 10, 10, 10, 10, 11, 12, 13, 14, 15, 15, 15, 15, 15, 15, 16, 17, 18, 19, 20, 21, 21, 21, 21, 21, 21, 21, 22, 23, 24, 25, 26, 27, 28, 28, 28, 28, 28, 28, 28, 28, 29, 30, 31, 32, 33, 34, 35, 36, 36, 36, 36, 36, 36, 36, 36, 36, 37, 38

Offset

1,3

Links

Paolo Xausa, Table of n, a(n) for n = 1..10000

Formula

a(n) = (1/2)*(n + A053615(n)).

Mathematica

A037458[n_] := A037458[n] = If[n == 1, 1, n - A037458[n - Floor[Sqrt[n]]]];
Array[A037458, 100] (* Paolo Xausa, Jun 22 2026 *)

Prog

(PARI) a(n)=if(n<2, 1, n-a(n-sqrtint(n)))

Crossrefs

Cf. A028391, A053615.

Sequence in context: A304110 A051134 A347777 * A296816 A064474 A379067

Adjacent sequences: A037455 A037456 A037457 * A037459 A037460 A037461

Keyword

nonn,changed

Author

Benoit Cloitre, Dec 22 2002

Extensions

Corrected by Franklin T. Adams-Watters, Oct 25 2006

Status

approved