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A097327
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Least positive integer m such that m*n has greater decimal digit length than n.
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2
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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
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listen;
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internal format)
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OFFSET
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1,1
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COMMENTS
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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).
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LINKS
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Michael S. Branicky, Table of n, a(n) for n = 1..10000
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FORMULA
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a(n) = A097326(n) + 1.
a(n) = ceiling(10^A055642(n)/n). - Michael S. Branicky, Oct 05 2021
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EXAMPLE
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a(12) = 9 since 12 has two decimal digits and 9*12 = 108 has three (but 8*12 = 96 has only two).
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PROG
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(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
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CROSSREFS
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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
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KEYWORD
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base,easy,nonn
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AUTHOR
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Rick L. Shepherd, Aug 04 2004
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STATUS
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approved
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