A165301 a(n) is the smallest number not already in the sequence, such that the concatenation of all a(n) displays the periodic digit string 1, 2, 3 (and repeat).

1, 2, 3, 12, 31, 23, 123, 1231, 231, 2312, 312, 3123, 12312, 31231, 23123, 123123, 1231231, 231231, 2312312, 312312, 3123123, 12312312, 31231231, 23123123, 123123123, 1231231231, 231231231, 2312312312, 312312312, 3123123123, 12312312312, 31231231231

Offset: 1

Author

Paolo P. Lava and Giorgio Balzarotti, Sep 14 2009

Keywords

• easy
• base
• nonn

Examples

			Starting from 1, 2, 3, the next number must be 12 because we need to continue with a 1. But 1 is already in the sequence so we need to attach a 2 -> 12. And so on.
		

Crossrefs

Cf. A165300, A165302-A165307.

Programs

Maple

cyc3 := proc(n) op(n,[2,3,1]) ; end:
A165301 := proc(n) option remember ; local k,prev,d,a ; if n = 1 then 1; else d := cyc3(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 := cyc3(d) ; a := 10*a+d ; end do; end if ; end proc:
seq(A165301(n),n=1..60) ; # R. J. Mathar, Oct 16 2009

Extensions

Keyword:base added, sequence extended by R. J. Mathar, Oct 16 2009