A025742 Index of 10^n within the sequence of the numbers of the form 4^i*10^j.

1, 3, 7, 12, 19, 28, 38, 50, 64, 79, 96, 115, 135, 157, 181, 206, 233, 262, 292, 324, 358, 393, 430, 469, 509, 551, 595, 640, 687, 736, 786, 838, 892, 947, 1004, 1063, 1123, 1185, 1249, 1314, 1381, 1450, 1520, 1592, 1666, 1741, 1818, 1897, 1977, 2059, 2143, 2228

Offset

0,2

Comments

Indices m for which A025649(m) is 0. - Michel Marcus, Jan 10 2018

Links

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

Formula

From Amiram Eldar, Nov 14 2025: (Start)

A025621(a(n)) = 10^n.

a(n) = 1 + Sum_{k=0..n} ceiling(k * c), where c = log_4(10) (A154155).

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

Example

The index of 10^0 in A025621 is 1, so a(0) = 1.
The index of 10^1 in A025621 is 3, so a(1) = 3.
The index of 10^2 in A025621 is 7, so a(2) = 7.

Mathematica

Accumulate[Table[Ceiling[n / Log10[4]], {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, 4)); \\ Charles R Greathouse IV, Jan 10 2018
(PARI) first(n)=my(s, N=1/10); vector(n+1, i, s+=logint(N*=10, 4)+1) \\ Charles R Greathouse IV, Jan 10 2018

Crossrefs

Cf. A011557, A025621, A025649, A025686, A154155.

Sequence in context: A283733 A025713 A022791 * A122793 A337300 A062714

Adjacent sequences: A025739 A025740 A025741 * A025743 A025744 A025745

Keyword

nonn,easy

Author

David W. Wilson

Extensions

Offset changed by Michel Marcus, Jan 10 2018

Status

approved