A165306 a(n) is the smallest number not yet in the sequence such that concatenation of all terms yields an infinite periodic stream of digits 1, 2, 3, ..., 8 (repeat from 1).

1, 2, 3, 4, 5, 6, 7, 8, 12, 34, 56, 78, 123, 45, 67, 81, 23, 456, 781, 234, 567, 812, 345, 678, 1234, 5678, 12345, 6781, 2345, 67812, 3456, 7812, 34567, 8123, 4567, 81234, 56781, 23456, 78123, 45678, 123456, 781234, 567812, 345678, 1234567, 812345

Offset: 1

Author

Paolo P. Lava and Giorgio Balzarotti, Sep 14 2009

Keywords

• easy
• nonn
• base

Examples

			Considering a(9), having already 1,2,3,4,5,6,7,8, the next number must be 12 because after 1,2,3,4,5,6,7,8 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-A165305, A165307.

Programs

Maple

cyc8 := proc(n) op(n, [2, 3, 4, 5, 6, 7, 8, 1]) ; end:
A165306 := proc(n) option remember ; local k, prev, d, a ; if n = 1 then 1; else d := cyc8(procname(n-1) mod 10) ; a := d ; while true do prev := false; for k from 1 to n-1 do if procname(k) = a then prev := true; break; end if; end do; if not prev then return a; end if; d := cyc8(d) ; a := 10*a+d ; end do; end if ; end proc:
seq(A165306(n), n=1..60) ; # R. J. Mathar, Feb 02 2010

Extensions

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