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%I #21 Apr 20 2024 16:19:14
%S 1,1,2,1,3,1,4,2,5,2,6,3,7,1,8,4,9,3,10,5,11,1,12,6,13,4,14,7,15,2,16,
%T 8,17,5,18,9,19,2,20,10,21,6,22,11,23,3,24,12,25,7,26,13,27,1,28,14,
%U 29,8,30,15,31,4,32,16,33,9,34,17,35,3,36,18,37,10,38,19,39,5,40,20,41,11,42,21,43,1,44,22,45,12
%N a(n) = floor((A000265(1+(3*n))+5)/6), where A000265 gives the odd part of its argument.
%C When a(n) is applied to square array A257852 we obtain square array A002260, or in other words, a(n) applied to any odd number gives the index of the column where it is located in array A257852.
%H Antti Karttunen, <a href="/A371092/b371092.txt">Table of n, a(n) for n = 0..16384</a>
%F a(n) = a(4*n + 1) = a(16*n + 5) = a(64*n + 21) = ... = a(4^k * n + ((4^k)-1)/3).
%t A371092[n_] := With[{k = 3*n + 1}, Floor[(k/2^IntegerExponent[k, 2] + 5)/6]];
%t Array[A371092, 100, 0] (* _Paolo Xausa_, Apr 20 2024 *)
%o (PARI)
%o A000265(n) = (n>>valuation(n,2));
%o A371092(n) = floor((A000265(1+(3*n))+5)/6);
%Y Cf. A000265, A002260, A257852, A371101.
%Y Cf. also A371093.
%K nonn
%O 0,3
%A _Antti Karttunen_, Apr 19 2024
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