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A371092 a(n) = floor((A000265(3*n+1)+5)/6), where A000265 gives the odd part of its argument.

%I A371092 #37 Oct 25 2024 10:10:23
%S A371092 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 A371092 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 A371092 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 A371092 a(n) = floor((A000265(3*n+1)+5)/6), where A000265 gives the odd part of its argument.
%C A371092 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 A371092 Antti Karttunen, <a href="/A371092/b371092.txt">Table of n, a(n) for n = 0..16384</a>
%F A371092 a(n) = a(4*n + 1) = a(16*n + 5) = a(64*n + 21) = ... = a(4^k * n + ((4^k)-1)/3).
%p A371092 with(padic): A37109 := n -> floor(1/6*(3*n + 1)/2^ordp(3*n + 1, 2) + 5/6); seq(A37109(n), n = 0 .. 89); # _Miles Wilson_, Oct 10 2024
%t A371092 A371092[n_] := With[{k = 3*n + 1}, Floor[(k/2^IntegerExponent[k, 2] + 5)/6]];
%t A371092 Array[A371092, 100, 0] (* _Paolo Xausa_, Apr 20 2024 *)
%o A371092 (PARI)
%o A371092 A000265(n) = (n>>valuation(n,2));
%o A371092 A371092(n) = floor((A000265(1+(3*n))+5)/6);
%Y A371092 Cf. A000265, A002260, A007814, A257852, A371101.
%Y A371092 Cf. also A371093.
%K A371092 nonn
%O A371092 0,3
%A A371092 _Antti Karttunen_, Apr 19 2024