A078295 Smallest multiple of n whose digits can be re-arranged to be a substring of the cyclic concatenation 1234567890123435678901234...

1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 132, 12, 65, 56, 45, 32, 102, 54, 76, 120, 21, 132, 23, 120, 675, 78, 54, 56, 87, 120, 465, 32, 132, 34, 210, 324, 2109, 76, 78, 120, 123, 210, 43, 132, 45, 3542, 423, 432, 98, 123450, 102, 312, 901, 54, 1320, 56, 342, 3654, 354, 120

Offset

1,2

Comments

Numbers n such that n or some digit permutation of n is a substring of the cyclic concatenation of digits 1,2,3,4,5,6,7,8,9,0,1,2...

If a(n) contains more 1's than it contains 0's and n>10, then a(10n)=10a(n) - Sam Alexander, Oct 19 2003

Links

Table of n, a(n) for n=1..60.

Formula

If m>1, a(10^m) is obtained by starting with a string of m-1 1's, then concatenating a string of m-1 2's, then a string of m-1 3's, ..., a string of m-1 9's, then finally a string of m 0's. So a(1000)=112233445566778899000. Also, to get a(5*10^m) from a(10^m), m>1, just take the rightmost 5 and move it in front of the 9's, so a(5000)=112233445667788995000 - Sam Alexander, Oct 19 2003

Example

a(36) = 324, digits can be rearranged as 2,3,4. a(35) = 210, (0,1,2.)

Crossrefs

Sequence in context: A044912 A061378 A004872 * A326302 A004883 A004894

Adjacent sequences: A078292 A078293 A078294 * A078296 A078297 A078298

Keyword

base,nonn

Author

Amarnath Murthy, Nov 26 2002

Extensions

More terms from Sam Alexander, Oct 19 2003

Status

approved