A072400 (Factors of 4 removed from n) modulo 8.

1, 2, 3, 1, 5, 6, 7, 2, 1, 2, 3, 3, 5, 6, 7, 1, 1, 2, 3, 5, 5, 6, 7, 6, 1, 2, 3, 7, 5, 6, 7, 2, 1, 2, 3, 1, 5, 6, 7, 2, 1, 2, 3, 3, 5, 6, 7, 3, 1, 2, 3, 5, 5, 6, 7, 6, 1, 2, 3, 7, 5, 6, 7, 1, 1, 2, 3, 1, 5, 6, 7, 2, 1, 2, 3, 3, 5, 6, 7, 5, 1, 2, 3, 5, 5, 6, 7, 6, 1, 2, 3, 7, 5, 6, 7, 6

Offset

1,2

Comments

a(n) <> 7 iff n equals the sum of 3 integer squares.

a(A004215(k)) = 7 for k>0;

Links

Antti Karttunen, Table of n, a(n) for n = 1..10000

Eric Weisstein's World of Mathematics, Square Numbers.

Formula

a(n) = A065883(n) mod 8.

A072401(n) = 1 - A057427(7 - a(n)).

Example

From Michael De Vlieger, May 08 2017: (Start)
a(4) = 1 since 4 = 1 * 4^1 and 4 / 4^1 = 1; 1 = 1 (mod 8).
a(5) = 5 since it is not a multiple of 4; 5 = 5 (mod 8).
a(12) = 3 since 12 = 3 * 4^1 and 12 / 4^1 = 3; 3 = 3 (mod 8).
a(44) = 3 since 44 = 11 * 4^1 and 44 / 4^1 = 11; 3 = 11 (mod 8).
a(64) = 1 since 64 = 1 * 4^3 and 64 / 4^3 = 1; 1 = 1 (mod 8).
(End)

Mathematica

Array[Mod[If[Mod[#, 4] == 0, #/4^IntegerExponent[#, 4], #], 8] &, 96] (* Michael De Vlieger, May 08 2017 *)

Prog

(Python)
def A072400(n): return (n>>((~n&n-1).bit_length()&-2))&7 # Chai Wah Wu, Aug 01 2023

Crossrefs

Cf. A000378, A004215, A057427, A065883, A072401, A286366.

Sequence in context: A325978 A326049 A357684 * A007913 A366244 A083346

Adjacent sequences: A072397 A072398 A072399 * A072401 A072402 A072403

Keyword

nonn

Author

Reinhard Zumkeller, Jun 16 2002

Extensions

Offset corrected (from 0 to 1) by Antti Karttunen, May 08 2017

Status

approved