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

Author

Jaroslav Krizek, May 07 2011

Keywords

• nonn
• easy
• base

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

Examples

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

Links

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

Crossrefs

Cf. A187285.

Programs

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

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

Formula

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