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A097326
Largest integer m such that m*n has the same decimal digit length as n.
3
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
FORMULA
a(n) = A097327(n) - 1.
a(n) = floor((10^A055642(n) - 1)/n). - 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 *)
Table[Ceiling[10^IntegerLength[n]/n] - 1, {n, 100}] (* Paolo Xausa, Nov 06 2024 *)
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
KEYWORD
base,easy,nonn,changed
AUTHOR
Rick L. Shepherd, Aug 04 2004
STATUS
approved