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A097326 Largest integer m such that m*n has the same decimal digit length as n. 2
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 (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 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

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Last modified February 4 14:43 EST 2023. Contains 360055 sequences. (Running on oeis4.)