A025741 Index of 10^n within the sequence of the numbers of the form 3^i*10^j.

1, 4, 9, 16, 25, 36, 49, 64, 81, 100, 121, 145, 171, 199, 229, 261, 295, 331, 369, 409, 451, 496, 543, 592, 643, 696, 751, 808, 867, 928, 991, 1056, 1124, 1194, 1266, 1340, 1416, 1494, 1574, 1656, 1740, 1826, 1915, 2006, 2099, 2194, 2291, 2390, 2491, 2594, 2699

Offset

0,2

Comments

Positions of zeros in A025644. - 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 14 2025: (Start)

A025616(a(n)) = 10^n.

a(n) = 1 + Sum_{k=0..n} ceiling(k * c), where c = log_3(10) (A152566).

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

Mathematica

Accumulate[Table[Ceiling[n / Log10[3]], {n, 0, 60}]] + 1 (* Amiram Eldar, Nov 14 2025 *)

Prog

(PARI) a(n)=my(N=1); n+1+sum(i=1, n, logint(N*=10, 3)); \\ Charles R Greathouse IV, Jan 10 2018
(PARI) first(n)=my(s, N=1/10); vector(n, i, s+=logint(N*=10, 3)+1) \\ Charles R Greathouse IV, Jan 10 2018

Crossrefs

Cf. A011557, A025616, A025644, A152566.

Sequence in context: A221222 A144913 A018885 * A387918 A384517 A179459

Adjacent sequences: A025738 A025739 A025740 * A025742 A025743 A025744

Keyword

nonn,easy

Author

David W. Wilson

Extensions

Offset corrected by Amiram Eldar, Nov 14 2025

Status

approved