A025747 Index of 10^n within the sequence of the numbers of the form 9^i*10^j.

1, 3, 6, 10, 15, 21, 28, 36, 45, 55, 66, 78, 91, 105, 120, 136, 153, 171, 190, 210, 231, 254, 278, 303, 329, 356, 384, 413, 443, 474, 506, 539, 573, 608, 644, 681, 719, 758, 798, 839, 881, 924, 969, 1015, 1062, 1110, 1159, 1209, 1260, 1312, 1365, 1419, 1474, 1530, 1587

Offset

0,2

Comments

Positions of zeros in A025683. - R. J. Mathar, Jul 06 2025

Links

Amiram Eldar, Table of n, a(n) for n = 0..10000 (terms 0..2000 from Robert Israel)

Formula

From Amiram Eldar, Nov 14 2025: (Start)

A025635(a(n)) = 10^n.

a(n) = 1 + Sum_{k=0..n} ceiling(k * c), where c = log_9(10) (A154160).

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

Maple

N:= 10^60: # for a(0)..a(log[10](N))
L:= sort([seq(seq(9^i*10^j, j=0..ilog10(N/9^i)), i=0..floor(log[9](N)))]):
select(t -> L[t] mod 9 <> 0, [$1..nops(L)]); # Robert Israel, May 12 2020

Mathematica

Accumulate[Table[Ceiling[n / Log10[9]], {n, 0, 60}]] + 1 (* Amiram Eldar, Nov 14 2025 *)

Crossrefs

Cf. A011557, A022330, A025635, A025683, A154160.

Sequence in context: A105340 A176659 A109811 * A025738 A078256 A025731

Adjacent sequences: A025744 A025745 A025746 * A025748 A025749 A025750

Keyword

nonn,easy

Author

David W. Wilson

Extensions

Offset corrected by Robert Israel, May 12 2020

Status

approved