A190302 - OEIS

%I #14 Jul 28 2018 10:40:15

%S 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,

%T 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,

%U 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

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

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

%C Conjecture: a(n) < 6 for all n (verified to n = 10022141). - _Felix Fröhlich_, Jul 28 2018

%H Nathaniel Johnston, <a href="/A190302/b190302.txt">Table of n, a(n) for n = 1..10000</a>

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

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

%p 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

%o (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

%Y Cf. A187285.

%K nonn,easy,base

%O 1,2

%A _Jaroslav Krizek_, May 07 2011