A110732 Let n = abc... where a,b,c ... are the digits. Then a(n) = least multiple of n of the form aaa...bbb...ccc..., with each digit having the same frequency f > 1; or 0 if no such number exists.

11, 22, 33, 44, 55, 66, 77, 88, 99, 1100, 1111, 0, 111111333333, 111111444444, 1155, 0, 11111111111111117777777777777777, 1188, 111111111111111111999999999999999999, 2200, 222222111111, 2222, 22222222222222222222223333333333333333333333, 0, 0

Offset

1,1

Comments

For odd n not a multiple of 5, a(n) is not 0, as every such odd number divides a (infinitely many) unary number of the type 11111...= (10^k-1)/9, by Fermat's little theorem. E.g., 13 divides 111111, hence a(13) = 111111333333. Zeros occur only for some powers/multiples of 2 and 5 as 25 does not divide 222555... etc. and 16 cannot divide any number of the type 111...666...

References

Amarnath Murthy, On the divisors of unary sequence, Smarandache Notions Journal, Vol-11, 2000.

Links

Table of n, a(n) for n=1..25.

Crossrefs

Cf. A110733.

Sequence in context: A020338 A052191 A321536 * A044836 A338754 A033008

Adjacent sequences: A110729 A110730 A110731 * A110733 A110734 A110735

Keyword

base,easy,nonn

Author

Amarnath Murthy, Aug 09 2005

Extensions

More terms from Franklin T. Adams-Watters, Jun 06 2006

Status

approved