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

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, 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, 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

Offset: 0

Author

Antti Karttunen, Apr 19 2024

Keywords

• nonn

Comments

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.

Links

• Antti Karttunen, Table of n, a(n) for n = 0..16384

Crossrefs

Cf. A000265, A002260, A007814, A257852, A371101.

Cf. also A371093.

Programs

Maple

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

Mathematica

A371092[n_] := With[{k = 3*n + 1}, Floor[(k/2^IntegerExponent[k, 2] + 5)/6]];
Array[A371092, 100, 0] (* Paolo Xausa, Apr 20 2024 *)

PARI

A000265(n) = (n>>valuation(n,2));
A371092(n) = floor((A000265(1+(3*n))+5)/6);

Formula

a(n) = a(4*n + 1) = a(16*n + 5) = a(64*n + 21) = ... = a(4^k * n + ((4^k)-1)/3).