cp's OEIS Frontend

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

%I A072400 #24 May 15 2025 00:50:00
%S A072400 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 A072400 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 A072400 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 A072400 (Factors of 4 removed from n) modulo 8.
%C A072400 a(n) <> 7 iff n equals the sum of 3 integer squares.
%C A072400 a(A004215(k)) = 7 for k>0;
%H A072400 Antti Karttunen, <a href="/A072400/b072400.txt">Table of n, a(n) for n = 1..10000</a>
%H A072400 Eric Weisstein's World of Mathematics, <a href="https://mathworld.wolfram.com/SquareNumber.html">Square Numbers</a>.
%F A072400 a(n) = A065883(n) mod 8.
%F A072400 A072401(n) = 1 - A057427(7 - a(n)).
%F A072400 Asymptotic mean: Limit_{m->oo} (1/m) * Sum_{k=1..m} a(k) = 4. - _Amiram Eldar_, May 15 2025
%e A072400 From _Michael De Vlieger_, May 08 2017: (Start)
%e A072400 a(4) = 1 since 4 = 1 * 4^1 and 4 / 4^1 = 1; 1 = 1 (mod 8).
%e A072400 a(5) = 5 since it is not a multiple of 4; 5 = 5 (mod 8).
%e A072400 a(12) = 3 since 12 = 3 * 4^1 and 12 / 4^1 = 3; 3 = 3 (mod 8).
%e A072400 a(44) = 3 since 44 = 11 * 4^1 and 44 / 4^1 = 11; 3 = 11 (mod 8).
%e A072400 a(64) = 1 since 64 = 1 * 4^3 and 64 / 4^3 = 1; 1 = 1 (mod 8). (End)
%t A072400 Array[Mod[If[Mod[#, 4] == 0, #/4^IntegerExponent[#, 4], #], 8] &, 96] (* _Michael De Vlieger_, May 08 2017 *)
%o A072400 (Python)
%o A072400 def A072400(n): return (n>>((~n&n-1).bit_length()&-2))&7 # _Chai Wah Wu_, Aug 01 2023
%o A072400 (PARI) a(n) = (n >> (2*valuation(n, 4))) % 8; \\ _Amiram Eldar_, May 15 2025
%Y A072400 Cf. A000378, A004215, A057427, A065883, A072401, A286366.
%K A072400 nonn,easy
%O A072400 1,2
%A A072400 _Reinhard Zumkeller_, Jun 16 2002
%E A072400 Offset corrected (from 0 to 1) by _Antti Karttunen_, May 08 2017