A097326 Largest integer m such that m*n has the same decimal digit length as n.

9, 4, 3, 2, 1, 1, 1, 1, 1, 9, 9, 8, 7, 7, 6, 6, 5, 5, 5, 4, 4, 4, 4, 4, 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, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 9, 9, 9, 9, 9, 9

Offset

1,1

Comments

For any positive base B >= 2 the corresponding sequence contains only terms from 1 to B-1 inclusive so the corresponding sequence for binary is all 1's (A000012).

Links

Michael De Vlieger, Table of n, a(n) for n = 1..10000

Formula

a(n) = A097327(n) - 1.

a(n) = floor(10^A055642(n) - 1). - Michael S. Branicky, Oct 05 2021

Example

a(12)=8 as 12 and 8*12=96 both have two decimal digits while 9*12=108 has three.

Mathematica

limn[n_]:=Module[{k=9, len=IntegerLength[n]}, While[IntegerLength[k*n] > len, k--]; k]; Array[limn, 110] (* Harvey P. Dale, Apr 28 2018 *)

Prog

(Python)
def a(n): return (10**len(str(n))-1)//n
print([a(n) for n in range(1, 106)]) # Michael S. Branicky, Oct 05 2021
(PARI) a(n) = my(m=1, sn=#Str(n)); while (#Str(m*n) <= sn, m++); m-1; \\ Michel Marcus, Oct 05 2021

Crossrefs

Cf. A061601 (analog for decimal m+n), A035327 (analog for binary m+n), A097327.

Cf. A055642.

Sequence in context: A223709 A050016 A033329 * A282100 A199965 A021110

Adjacent sequences: A097323 A097324 A097325 * A097327 A097328 A097329

Keyword

base,easy,nonn

Author

Rick L. Shepherd, Aug 04 2004

Status

approved