A025702 Index of 4^n within the sequence of the numbers of the form 4^i*5^j.

1, 2, 4, 7, 11, 16, 22, 29, 36, 44, 53, 63, 74, 86, 99, 112, 126, 141, 157, 174, 192, 211, 230, 250, 271, 293, 316, 340, 365, 390, 416, 443, 471, 500, 530, 561, 593, 625, 658, 692, 727, 763, 800, 838, 876, 915, 955, 996, 1038, 1081, 1125, 1169, 1214, 1260, 1307, 1355

Offset

0,2

Comments

Positions of zeros in A025650. - 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)) = 4^n.

a(n) = 1 + Sum_{k=0..n} ceiling(k * c), where c = log_5(4) = A153101.

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

Mathematica

Accumulate[Table[Ceiling[n * Log[5, 4]], {n, 0, 60}]] + 1 (* Amiram Eldar, Nov 13 2025 *)

Prog

(PARI) a(n)=my(N=1); n+1+sum(i=1, n, logint(N<<=2, 5)); \\ Charles R Greathouse IV, Jan 11 2018
(PARI) first(n)=my(s, N=1/4); vector(n+1, i, s+=logint(N<<=2, 5)+1) \\ Charles R Greathouse IV, Jan 11 2018

Crossrefs

Differs from A025717 at a(65).

Cf. A000302, A025617, A025650, A153101.

Sequence in context: A024224 A025727 A319159 * A025717 A348575 A348400

Adjacent sequences: A025699 A025700 A025701 * A025703 A025704 A025705

Keyword

nonn,easy

Author

David W. Wilson

Extensions

Offset corrected by Charles R Greathouse IV, Jan 11 2018

Status

approved