A097327 - OEIS

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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

(list; graph; refs; listen; history; text; internal format)

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