A165305 a(n) is the smallest number not yet in the sequence such that the concatenation of all terms yields a periodic stream of digits 1, 2, 3, ..., 7 (repeat from 1).

1, 2, 3, 4, 5, 6, 7, 12, 34, 56, 71, 23, 45, 67, 123, 456, 712, 345, 671, 234, 567, 1234, 5671, 2345, 6712, 3456, 7123, 4567, 12345, 67123, 45671, 23456, 71234, 56712, 34567, 123456, 712345, 671234, 567123, 456712, 345671, 234567, 1234567

Offset: 1

Author

Paolo P. Lava and Giorgio Balzarotti, Sep 14 2009

Keywords

• easy
• base
• nonn

Examples

			For a(8), having already 1, 2, 3, 4, 5, 6, 7, the next number must be 12 because after 1,2,3,4,5,6,7 we shall continue with a 1.
But 1 is already in the sequence so we need to add a 2 -> 12. And so on.
		

Crossrefs

Cf. A165300-A165304, A165306, A165307

Extensions

Keyword base added by R. J. Mathar, Feb 02 2010