A025706 Index of 5^n within the sequence of the numbers of the form 4^i*5^j.

1, 3, 6, 10, 15, 21, 28, 37, 47, 58, 70, 83, 97, 113, 130, 148, 167, 187, 208, 231, 255, 280, 306, 333, 361, 391, 422, 454, 487, 521, 556, 592, 630, 669, 709, 750, 792, 835, 880, 926, 973, 1021, 1070, 1120, 1172, 1225, 1279, 1334, 1390, 1447, 1506, 1566, 1627, 1689

Offset

0,2

Comments

Positions of zeros in A025646. - 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)

A025617(a(n)) = 5^n.

a(n) = 1 + Sum_{k=0..n} ceiling(k * c), where c = log_4(5) (A153201).

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

Mathematica

Accumulate[Table[Ceiling[n * Log[4, 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, 4)); \\ Charles R Greathouse IV, Jan 11 2018
(PARI) first(n)=my(s, N=1/5); vector(n+1, i, s+=logint(N*=5, 4)+1) \\ Charles R Greathouse IV, Jan 11 2018

Crossrefs

Cf. A000351, A025617, A025646, A153201.

Differs from A025730 at a(56).

Sequence in context: A120721 A122056 A358038 * A025730 A384328 A392544

Adjacent sequences: A025703 A025704 A025705 * A025707 A025708 A025709

Keyword

nonn,easy

Author

David W. Wilson

Extensions

Offset corrected by Charles R Greathouse IV, Jan 11 2018

Status

approved