A165304 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, 4, 5, 6 (and repeat).

1, 2, 3, 4, 5, 6, 12, 34, 56, 123, 45, 61, 23, 456, 1234, 561, 234, 5612, 345, 612, 3456, 12345, 6123, 4561, 2345, 61234, 56123, 45612, 34561, 23456, 123456, 1234561, 234561, 2345612, 345612, 3456123, 456123, 4561234, 561234, 5612345, 612345, 6123456, 12345612

Offset

1,2

Links

Table of n, a(n) for n=1..43.

Example

Starting from 1, 2, 3, 4, 5, 6, the next number must be 12 because the leading digit must be a 1. But 1 is already in the sequence so we need to attach a 2 -> 12.

Maple

cyc6 := proc(n) op(n, [2, 3, 4, 5, 6, 1]) ; end:
A165304 := proc(n) option remember ; local k, prev, d, a ; if n = 1 then 1; else d := cyc6(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 := cyc6(d) ; a := 10*a+d ; end do; end if ; end proc:
seq(A165304(n), n=1..60) ; # R. J. Mathar, Oct 16 2009

Crossrefs

Cf. A165300-A165303, A165305-A165307.

Sequence in context: A125141 A350211 A282505 * A266642 A245450 A115307

Adjacent sequences: A165301 A165302 A165303 * A165305 A165306 A165307

Keyword

easy,nonn,base

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