%I #18 Aug 01 2023 15:14:25
%S 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,
%T 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,
%U 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
%N (Factors of 4 removed from n) modulo 8.
%C a(n) <> 7 iff n equals the sum of 3 integer squares.
%C a(A004215(k)) = 7 for k>0;
%H Antti Karttunen, <a href="/A072400/b072400.txt">Table of n, a(n) for n = 1..10000</a>
%H Eric Weisstein's World of Mathematics, <a href="http://mathworld.wolfram.com/SquareNumber.html">Square Numbers.</a>
%F a(n) = A065883(n) mod 8.
%F A072401(n) = 1 - A057427(7 - a(n)).
%e From _Michael De Vlieger_, May 08 2017: (Start)
%e a(4) = 1 since 4 = 1 * 4^1 and 4 / 4^1 = 1; 1 = 1 (mod 8).
%e a(5) = 5 since it is not a multiple of 4; 5 = 5 (mod 8).
%e a(12) = 3 since 12 = 3 * 4^1 and 12 / 4^1 = 3; 3 = 3 (mod 8).
%e a(44) = 3 since 44 = 11 * 4^1 and 44 / 4^1 = 11; 3 = 11 (mod 8).
%e a(64) = 1 since 64 = 1 * 4^3 and 64 / 4^3 = 1; 1 = 1 (mod 8).
%e (End)
%t Array[Mod[If[Mod[#, 4] == 0, #/4^IntegerExponent[#, 4], #], 8] &, 96] (* _Michael De Vlieger_, May 08 2017 *)
%o (Python)
%o def A072400(n): return (n>>((~n&n-1).bit_length()&-2))&7 # _Chai Wah Wu_, Aug 01 2023
%Y Cf. A000378, A004215, A057427, A065883, A072401, A286366.
%K nonn
%O 1,2
%A _Reinhard Zumkeller_, Jun 16 2002
%E Offset corrected (from 0 to 1) by _Antti Karttunen_, May 08 2017