A097327 Least positive integer m such that m*n has greater decimal digit length than n.

10, 5, 4, 3, 2, 2, 2, 2, 2, 10, 10, 9, 8, 8, 7, 7, 6, 6, 6, 5, 5, 5, 5, 5, 4, 4, 4, 4, 4, 4, 4, 4, 4, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 10, 10, 10

Offset

1,1

Comments

For any positive base B >= 2 the corresponding sequence contains only terms from 2 to B inclusive so the corresponding sequence for binary is all 2s (A007395).

Links

Michael S. Branicky, Table of n, a(n) for n = 1..10000

Formula

a(n) = A097326(n) + 1.

a(n) = ceiling(10^A055642(n)/n). - Michael S. Branicky, Oct 05 2021

Example

a(12) = 9 since 12 has two decimal digits and 9*12 = 108 has three (but 8*12 = 96 has only two).

Mathematica

Table[Ceiling[10^IntegerLength[n]/n], {n, 100}] (* Paolo Xausa, Nov 02 2024 *)

Prog

(Python)
def a(n): return (10**len(str(n))-1)//n + 1
print([a(n) for n in range(1, 103)]) # Michael S. Branicky, Oct 05 2021
(PARI) a(n) = my(m=1, sn=#Str(n)); while (#Str(m*n) <= sn, m++); m; \\ Michel Marcus, Oct 05 2021

Crossrefs

Cf. A089186 (analog for decimal m+n), A080079 (analog for binary m+n), A097326.

Cf. A055642.

Sequence in context: A134167 A080461 A066578 * A226583 A007272 A061280

Adjacent sequences: A097324 A097325 A097326 * A097328 A097329 A097330

Keyword

base,easy,nonn

Author

Rick L. Shepherd, Aug 04 2004

Status

approved