A079847 Smallest multiple of n in which the string of digits of n occurs after (n-1) most significant digits.

1, 12, 123, 1004, 10005, 100026, 1000027, 10000008, 100000089, 10000000010, 100000000111, 1000000000212, 10000000000913, 100000000000614, 1000000000000215, 10000000000000016, 100000000000000517, 1000000000000000818, 10000000000000001719, 100000000000000000020

Offset

1,2

Links

Alois P. Heinz, Table of n, a(n) for n = 1..1000

Formula

For n>1, let d be the number of digits in n, and n' = n/gcd(n,10^d). Then a(n) = (10^{n-2}+mod(-(10^{n-2}),n')) * 10^d + n. (The mod function used here always returns a nonnegative result; e.g., mod(-2,7) = 5.) - Franklin T. Adams-Watters, Jul 25 2014

Example

a(4) = 1004, 4 occurs as the 4th digit from the left. a(10) = 10000000010. ('10') occurs after 9 digits.

Mathematica

a079847[n_] := 10^(n - 1 + Floor[Log10[n]]) + (NestWhile[# + 1 &, 0, Mod[10^(n - 1 + Floor[Log10[n]]) + # 10^(1 + Floor[Log10[n]]), n] != 0 &]) 10^(1 + Floor[Log10[n]]) + n; a079847[1] = 1; Table[a079847[n], {n, 20}] (* L. Edson Jeffery, Jul 16 2014 *)

Prog

(PARI) numdig(n)=my(r=1); while(n>=10, n\=10; r++); r
a(n) = my(k, m); if(n<=1, n, k=10^numdig(n); m=10^(n-2); (-m%(n\gcd(n, k))+m)*k+n) \\ Franklin T. Adams-Watters, Jul 25 2014

Crossrefs

Cf. A245470.

Sequence in context: A001703 A127422 A278983 * A144165 A113572 A037701

Adjacent sequences: A079844 A079845 A079846 * A079848 A079849 A079850

Keyword

base,nonn

Author

Amarnath Murthy, Feb 18 2003

Extensions

More terms from Antonio G. Astudillo (afg_astudillo(AT)lycos.com), Jul 04 2003

Status

approved