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A331470 a(n) is the greatest value of the form s_1^2 + ... + s_k^2 such that the concatenation of the binary representations of s_1^2, ..., s_k^2 equals the binary representation of n.

%I A331470 #11 Jan 19 2020 06:27:49
%S A331470 0,1,1,2,4,2,2,3,4,9,2,3,5,3,3,4,16,5,9,10,5,3,3,4,5,25,3,4,6,4,4,5,
%T A331470 16,17,5,6,36,10,10,11,5,10,3,4,6,4,4,5,17,49,25,26,6,4,4,5,6,26,4,5,
%U A331470 7,5,5,6,64,17,17,18,8,6,6,7,36,37,10,11,13,11
%N A331470 a(n) is the greatest value of the form s_1^2 + ... + s_k^2 such that the concatenation of the binary representations of s_1^2, ..., s_k^2 equals the binary representation of n.
%C A331470 This sequence is a variant of A331362.
%H A331470 Rémy Sigrist, <a href="/A331470/b331470.txt">Table of n, a(n) for n = 0..8192</a>
%H A331470 Rémy Sigrist, <a href="/A331470/a331470.gp.txt">PARI program for A331470</a>
%H A331470 <a href="/index/Bi#binary">Index entries for sequences related to binary expansion of n</a>
%F A331470 a(n) >= A000120(n) with equality iff n belongs to A003754.
%F A331470 a(n^2) = n^2.
%e A331470 For n = 12:
%e A331470 - the binary representation of 12 is "1100",
%e A331470 - we can split it into "1" and "1" and "0" and "0" (1^2 and 1^2 and 0^2 and 0^2),
%e A331470 - or into "1" and "100" (1^2 and 2^2),
%e A331470 - hence a(12) = max(2, 5) = 5.
%o A331470 (PARI) See Links section.
%Y A331470 Cf. A000120, A003754, A331362.
%K A331470 nonn,base
%O A331470 0,4
%A A331470 _Rémy Sigrist_, Jan 17 2020