A025723 Index of 7^n within sequence of numbers of form 5^i*7^j.

1, 3, 6, 10, 15, 22, 30, 39, 49, 60, 73, 87, 102, 118, 135, 154, 174, 195, 217, 240, 265, 291, 318, 346, 376, 407, 439, 472, 506, 542, 579, 617, 656, 696, 738, 781, 825, 870, 916, 964, 1013, 1063, 1114, 1166, 1220, 1275, 1331, 1388, 1447, 1507, 1568, 1630, 1693

Offset: 0

Author

David W. Wilson

Keywords

• nonn
• easy

Comments

Positions of zeros in A025652. - R. J. Mathar, Jul 06 2025

Links

• Robert Israel, Table of n, a(n) for n = 0..10000

Crossrefs

Cf. A025708, A022330, A022331, etc.

Programs

Maple

ListTools:-PartialSums([1,seq(ceil(k*log[5](7)),k=1..100)]); # Robert Israel, Nov 16 2016

Mathematica

Table[1 + Sum[Ceiling[k Log[5, 7]], {k, n}], {n, 0, 52}] (* Michael De Vlieger, Nov 16 2016 *)

PARI

a(n)=my(N=1); n+1+sum(i=1, n, logint(N*=7, 5)); \\ Charles R Greathouse IV, Jan 11 2018

PARI

first(n)=my(s, N=1/7); vector(n+1, i, s+=logint(N*=7, 5)+1) \\ Charles R Greathouse IV, Jan 11 2018

Formula

a(n) = 1 + Sum_{k=1..n} ceiling(k*log_5(7)). - Robert Israel, Nov 16 2016

Extensions

Offset changed to 0 by Robert Israel, Nov 16 2016