A190302 Smallest number h such that the decimal expansion of n*h starts with 1.

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

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