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

1,2

Links

Table of n, a(n) for n=1..32.

Example

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.

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

Crossrefs

Cf. A165300, A165302-A165307.

Sequence in context: A073617 A034381 A076424 * A072440 A135522 A353831

Adjacent sequences: A165298 A165299 A165300 * A165302 A165303 A165304

Keyword

easy,base,nonn

Author

Paolo P. Lava and Giorgio Balzarotti, Sep 14 2009

Extensions

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

Status

approved