A141027 a(n) = smallest number m which without its leftmost digit is equal to m/n (or 0 if no such number exists).

0, 15, 0, 25, 12, 35, 0, 45, 0, 11, 0, 65, 0, 75, 32, 85, 0, 95, 0, 21, 0, 0, 0, 625, 52, 0, 0, 725, 0, 31, 0, 825, 0, 0, 72, 925, 0, 0, 0, 41, 0, 0, 0, 0, 92, 0, 0, 6125, 0, 51, 0, 0, 0, 0, 0, 7125, 0, 0, 0, 61, 0, 0, 0, 8125, 0, 0, 0, 0, 0, 71, 0, 9125, 0, 0, 304, 0, 0, 0, 0, 81, 0, 0, 0

Offset

2,2

Links

Table of n, a(n) for n=2..84.

Formula

For n>10, a(n) is nonzero only if n-1 divides k*10^s for some positive integers k<=9 and s. For minimum such number k*10^s, we have a(n) = n*k*10^s/(n-1). - Max Alekseyev, Apr 13 2009

Example

a(7) = 35: 35/7 = 5 = 35 with leftmost digit deleted.

Prog

(PARI) { a(n) = if(n<=10, return([0, 0, 15, 0, 25, 12, 35, 0, 45, 0][n])); t=[valuation(n-1, 2), valuation(n-1, 5)]; k=(n-1)\2^t[1]\5^t[2]; if(k>9, return(0)); while(t[1]>t[2]&&2*k<=9, k*=2; t[1]--); while(t[1]<t[2]&&5*k<=9, k*=5; t[2]--); (k*10^vecmax(t)*n)\(n-1) } \\ Max Alekseyev, Apr 13 2009

Crossrefs

Sequence in context: A055965 A067154 A187486 * A186436 A054670 A277929

Adjacent sequences: A141024 A141025 A141026 * A141028 A141029 A141030

Keyword

nonn,base

Author

Lekraj Beedassy, Jul 29 2008

Extensions

Corrected and extended by Max Alekseyev, Apr 13 2009

Status

approved