A127427 a(n) = v_3( (6n)! ) - v_3( (3n)! ), where v_3(N) is the 3-adic valuation A007949(N).

0, 1, 3, 4, 5, 8, 9, 10, 12, 13, 14, 16, 17, 18, 22, 23, 24, 26, 27, 28, 30, 31, 32, 35, 36, 37, 39, 40, 41, 43, 44, 45, 48, 49, 50, 52, 53, 54, 56, 57, 58, 63, 64, 65, 67, 68, 69, 71, 72, 73, 76, 77, 78, 80, 81, 82, 84, 85, 86, 89, 90, 91, 93, 94, 95, 97, 98, 99, 103, 104, 105, 107

Offset: 0

Author

N. J. A. Sloane, Apr 02 2007

Keywords

• nonn

Links

• Sung-Hyuk Cha, On Integer Sequences Derived from Balanced k-ary Trees, Applied Mathematics in Electrical and Computer Engineering, 2012. - From _N. J. A. Sloane_, Jun 12 2012
• Sung-Hyuk Cha, On Complete and Size Balanced k-ary Tree Integer Sequences, International Journal of Applied Mathematics and Informatics, Issue 2, Volume 6, 2012, pp. 67-75. - From _N. J. A. Sloane_, Dec 24 2012

Crossrefs

Cf. A007949, A053735, A054861, A004128.

Essentially partial sums of A127427.

Programs

Mathematica

s[n_] := Plus @@ IntegerDigits[n, 3]; a[n_] := (3*n + s[3*n] - s[6*n])/2; Array[a, 100, 0] (* Amiram Eldar, Feb 21 2021 *)

PARI

a(n) = valuation((6*n)!, 3) - valuation((3*n)!, 3); \\ Michel Marcus, Jul 29 2017

Formula

a(n) - n = a( [(n+1)/3] ).

a(n) = (3*n + A053735(n) - A053735(6*n))/2. - Amiram Eldar, Feb 21 2021