A072401 1 iff n is of the form 4^m*(8k+7).

0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 1, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 1, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 1, 0, 0, 1, 0

Offset: 0

Author

Reinhard Zumkeller, Jun 16 2002

Keywords

• nonn
• easy

Comments

Characteristic function of A004215, indicating numbers not the sum of 3 integer squares.

a(n) + 1 is the smallest positive number such that (a(n) + 1) * n is the sum of three squares. - Peter Schorn, Jul 18 2023

Links

• Jean-Paul Allouche and Jeffrey Shallit, The ring of k-regular sequences, Theoretical Computer Sci., 98 (1992), 163-197; preprint. See Example 20.
• Eric Weisstein's World of Mathematics, Square Numbers.
• Index entries for sequences related to sums of squares.
• Index entries for characteristic functions.

Crossrefs

Cf. A004215, A057427, A064873, A072400.

Cf. A071374.

Programs

Mathematica

A072400[n_] := Mod[If[Mod[n, 4] == 0, n/4^IntegerExponent[n, 4], n], 8];
a[n_] := 1 - Sign[7 - A072400[n]];
Table[a[n], {n, 0, 96}] (* Jean-François Alcover, Dec 13 2021 *)

PARI

a(n) = if(n, (n >> (2*valuation(n, 4))) % 8 == 7, 0); \\ Amiram Eldar, May 15 2025

Python

def A072401(n): return ((m:=(~n&n-1).bit_length())&1^1)&int((n>>m)&7==7) # Chai Wah Wu, Aug 01 2023

Formula

a(n) = 1 - A057427(7 - A072400(n)).

a(A004215(k)) = 1 for k>0.

a(n) = A057427(A064873(n)).

For n<112: a(n) = A064873(n), but A064873(112) = 2, as also a(112 - 1) = 1.

Asymptotic mean: Limit_{m->oo} (1/m) * Sum_{k=1..m} a(k) = 1/6. - Amiram Eldar, May 15 2025