A022331 Index of 2^n within sequence of numbers of form 2^i*3^j (A003586).

1, 2, 4, 6, 9, 13, 17, 22, 28, 34, 41, 48, 56, 65, 74, 84, 95, 106, 118, 130, 143, 157, 171, 186, 202, 218, 235, 253, 271, 290, 309, 329, 350, 371, 393, 416, 439, 463, 487, 512, 538, 564, 591, 619, 647, 676, 706, 736, 767, 798, 830, 863, 896, 930, 965, 1000, 1036, 1072

Offset: 0

Author

Clark Kimberling

Keywords

• nonn

Links

• Amiram Eldar, Table of n, a(n) for n = 0..10000 (terms 0..1000 from Zak Seidov)
• Norman Carey, Lambda Words: A Class of Rich Words Defined Over an Infinite Alphabet, arXiv preprint arXiv:1303.0888 [math.CO], 2013; Lambda Words: A Class of Rich Words Defined Over an Infinite Alphabet, J. Int. Seq. 16 (2013), Article 13.3.4.

Crossrefs

Cf. A000079, A003586, A071521, A020915 (first differences), A152747.

Cf. A022330 (index of 3^n within A003586).

Programs

Mathematica

c[0] = 1; c[n_] := 1 + Sum[Ceiling[j*Log[3, 2]], {j, n}]; Table[c[i], {i, 0, 60}] (* Norman Carey, Jun 13 2012 *)

PARI

a(n)=my(t=1);1+n+sum(k=1,n,logint(t*=2,3)) \\ Ruud H.G. van Tol, Nov 25 2022

Python

from sympy import integer_log
def A022331(n):
    m = 1<Chai Wah Wu, Sep 16 2024

Formula

a(n) = A071521(A000079(n)); A003586(a(n)) = A000079(n). - Reinhard Zumkeller, May 09 2006

a(n) ~ c * n^2, where c = log(2)/(2*log(3)) (A152747). - Amiram Eldar, Apr 07 2023