A025707 Index of 5^n within the sequence of the numbers of the form 5^i*6^j.

1, 2, 4, 7, 11, 16, 22, 29, 37, 46, 55, 65, 76, 88, 101, 115, 130, 146, 163, 181, 199, 218, 238, 259, 281, 304, 328, 353, 379, 406, 433, 461, 490, 520, 551, 583, 616, 650, 685, 721, 757, 794, 832, 871, 911, 952, 994, 1037, 1081, 1126, 1171, 1217, 1264, 1312, 1361

Offset

0,2

Comments

Positions of zeros in A025659. - R. J. Mathar, Jul 06 2025

Links

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

Formula

From Amiram Eldar, Nov 13 2025: (Start)

A025622(a(n)) = 5^n.

a(n) = 1 + Sum_{k=0..n} ceiling(k * c), where c = log_6(5) (A153202).

a(n) ~ c * n^2 / 2, where c is defined above. (End)

Mathematica

Accumulate[Table[Ceiling[n * Log[6, 5]], {n, 0, 60}]] + 1 (* Amiram Eldar, Nov 13 2025 *)

Prog

(PARI) a(n)=my(N=1); n+1+sum(i=1, n, logint(N*=5, 6)); \\ Charles R Greathouse IV, Jan 11 2018
(PARI) first(n)=my(s, N=1/5); vector(n+1, i, s+=logint(N*=5, 6)+1) \\ Charles R Greathouse IV, Jan 11 2018

Crossrefs

Cf. A000351, A025622, A025659, A153202.

Sequence in context: A348400 A025726 A070280 * A337919 A025733 A025716

Adjacent sequences: A025704 A025705 A025706 * A025708 A025709 A025710

Keyword

nonn,easy

Author

David W. Wilson

Extensions

Offset corrected by Charles R Greathouse IV, Jan 11 2018

Status

approved