A025693 Index of 2^n within the sequence of the numbers of the form 2^i*7^j.

1, 2, 3, 5, 7, 9, 12, 15, 18, 22, 26, 30, 35, 40, 45, 51, 57, 64, 71, 78, 86, 94, 102, 111, 120, 129, 139, 149, 159, 170, 181, 193, 205, 217, 230, 243, 256, 270, 284, 298, 313, 328, 343, 359, 375, 392, 409, 426, 444, 462, 480, 499, 518, 537, 557, 577, 597, 618, 639, 661, 683

Offset

0,2

Comments

Positions of zeros in A025664. - R. J. Mathar, Jul 06 2025

Links

Charles R Greathouse IV, Table of n, a(n) for n = 0..10000

Formula

a(n) ~ kn^2 + O(n) with k = log(2)/(2*log(7)). - Charles R Greathouse IV, Jun 28 2011 [corrected by Amiram Eldar, Nov 13 2025]

From Amiram Eldar, Nov 13 2025: (Start)

A003591(a(n)) = 2^n.

a(n) = 1 + Sum_{k=0..n} ceiling(k * c), where c = log_7(2) (A152713). (End)

Mathematica

Accumulate[Table[Ceiling[n * Log[7, 2]], {n, 0, 60}]] + 1 (* Amiram Eldar, Nov 13 2025 *)

Prog

(PARI) a(n)=my(N=7<<n); sum(k=0, log(N)\log(7)-1, #binary(N\=7)) \\ Charles R Greathouse IV, Jun 28 2011
(PARI) a(n)=my(N=1); n+1+sum(i=1, n, logint(N<<=1, 7)); \\ Charles R Greathouse IV, Jan 11 2018
(PARI) first(n)=my(s, N=1/2); vector(n+1, i, s+=logint(N<<=1, 7)+1) \\ Charles R Greathouse IV, Jan 11 2018

Crossrefs

Cf. A000079, A003591, A025664, A152713.

Sequence in context: A130518 A001840 A022794 * A117930 A090632 A022786

Adjacent sequences: A025690 A025691 A025692 * A025694 A025695 A025696

Keyword

nonn,easy

Author

David W. Wilson

Extensions

An incorrect g.f. was deleted by N. J. A. Sloane, Sep 16 2009

Status

approved