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

0,12

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

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)

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 *)

Prog

(Magma) A005130:=func<i | IsZero(i) select 1 else &*[Factorial(3*k+1)/Factorial(i+k): k in [0..i-1]]>; [Valuation(A005130(n), 3): n in [0..100]]; // Bruno Berselli, Aug 05 2013

Crossrefs

Cf. A005130, A007949, A053735, A194827.

Sequence in context: A082876 A096099 A019780 * A133293 A262565 A096289

Adjacent sequences: A227830 A227831 A227832 * A227834 A227835 A227836

Keyword

nonn

Author

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

Status

approved