A227833 3-adic valuation of A005130(n).

0, 0, 0, 0, 1, 1, 0, 0, 0, 0, 1, 2, 3, 5, 5, 3, 2, 1, 0, 0, 0, 0, 1, 1, 0, 0, 0, 0, 1, 2, 3, 5, 6, 6, 7, 8, 9, 11, 13, 15, 18, 18, 15, 13, 11, 9, 8, 7, 6, 6, 5, 3, 2, 1, 0, 0, 0, 0, 1, 1, 0, 0, 0, 0, 1, 2, 3, 5, 5, 3, 2, 1, 0, 0, 0, 0, 1, 1, 0, 0, 0, 0, 1, 2, 3, 5, 6, 6, 7, 8, 9, 11, 13, 15, 18, 19, 18, 18, 18, 18, 19

Offset: 0

Author

N. J. A. Sloane, Aug 04 2013, based on a suggestion from Victor H. Moll

Keywords

• nonn

Comments

3^a(n) is the highest power of 3 dividing A005130(n).

Links

• Amiram Eldar, Table of n, a(n) for n = 0..10000

Crossrefs

Cf. A005130, A007949, A053735, A194827.

Programs

Magma

A005130:=func; [Valuation(A005130(n),3): n in [0..100]]; // Bruno Berselli, Aug 05 2013

Mathematica

s[n_] := Plus @@ IntegerDigits[n, 3]; a[0] = 0; a[n_] := a[n] = a[n - 1] + (s[2*n - 2] + s[2*n - 1] - s[n - 1] - s[3*n - 2])/2; Array[a, 101, 0] (* Amiram Eldar, Feb 21 2021 *)

Formula

From Amiram Eldar, Feb 21 2021: (Start)

a(n) = A007949(A005130(n)).

a(n) = a(n-1) + (s(2*n-2) + s(2*n-1) - s(n-1) - s(3*n-2))/2, where s(n) = A053735(n). (End)