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A190302 Smallest number h such that the decimal expansion of n*h starts with 1. 2
1, 5, 4, 3, 2, 2, 2, 2, 2, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 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, 1, 1, 1, 1, 1, 1 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,2

COMMENTS

Quotient of the smallest multiple of n beginning with 1 (A187285(n)) and n.

Conjecture: a(n) < 6 for all n (verified to n = 10022141). - Felix Fröhlich, Jul 28 2018

LINKS

Nathaniel Johnston, Table of n, a(n) for n = 1..10000

FORMULA

a(n) = A187285(n) / n.

EXAMPLE

For n = 7: a(7) = 2 because 2 * 7 = 14. Number 14 is the smallest number beginning with 1 divisible by 7.

MAPLE

A190302 := proc(n) local d, h: for h from 1 do d:=convert(n*h, base, 10): if(d[nops(d)]=1)then return h: fi: od: end: seq(A190302(n), n=1..105); # Nathaniel Johnston, Jun 15 2011

PROG

(PARI) a(n) = my(h=1, inid=0); while(1, my(inid=digits(n*h)[1]); if(inid==1, return(h)); h++) \\ Felix Fröhlich, Jul 28 2018

CROSSREFS

Cf. A187285.

Sequence in context: A055116 A276373 A317173 * A223475 A190137 A003561

Adjacent sequences:  A190299 A190300 A190301 * A190303 A190304 A190305

KEYWORD

nonn,easy,base

AUTHOR

Jaroslav Krizek, May 07 2011

STATUS

approved

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Last modified February 24 10:37 EST 2020. Contains 332209 sequences. (Running on oeis4.)