A165302 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 (and repeat).

1, 2, 3, 4, 12, 34, 123, 41, 23, 412, 341, 234, 1234, 12341, 2341, 23412, 3412, 34123, 4123, 41234, 123412, 341234, 1234123, 412341, 234123, 4123412, 3412341, 2341234, 12341234, 123412341, 23412341, 234123412, 34123412, 341234123, 41234123, 412341234

Offset

1,2

Links

Table of n, a(n) for n=1..36.

Example

Starting from 1, 2, 3, 4, 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

cyc4 := proc(n) op(n, [2, 3, 4, 1]) ; end:
A165302 := proc(n) option remember ; local k, prev, d, a ; if n = 1 then 1; else d := cyc4(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 := cyc4(d) ; a := 10*a+d ; end do; end if ; end proc:
seq(A165302(n), n=1..60) ; # R. J. Mathar, Oct 16 2009

Crossrefs

Cf. A165300, A165301, A165303-A165307.

Sequence in context: A333620 A173446 A053350 * A276530 A360061 A251411

Adjacent sequences: A165299 A165300 A165301 * A165303 A165304 A165305

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