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
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
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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
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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.
Comments