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A127427
a(n) = v_3( (6n)! ) - v_3( (3n)! ), where v_3(N) is the 3-adic valuation A007949(N).
2
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
0,3
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
FORMULA
a(n) - n = a( [(n+1)/3] ).
a(n) = (3*n + A053735(n) - A053735(6*n))/2. - Amiram Eldar, Feb 21 2021
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 *)
PROG
(PARI) a(n) = valuation((6*n)!, 3) - valuation((3*n)!, 3); \\ Michel Marcus, Jul 29 2017
CROSSREFS
Essentially partial sums of A127427.
Sequence in context: A100614 A274231 A173999 * A286994 A047205 A283765
KEYWORD
nonn
AUTHOR
N. J. A. Sloane, Apr 02 2007
STATUS
approved