A165304 - OEIS

%I #6 May 05 2019 02:15:11

%S 1,2,3,4,5,6,12,34,56,123,45,61,23,456,1234,561,234,5612,345,612,3456,

%T 12345,6123,4561,2345,61234,56123,45612,34561,23456,123456,1234561,

%U 234561,2345612,345612,3456123,456123,4561234,561234,5612345,612345,6123456,12345612

%N 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).

%e 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.

%p cyc6 := proc(n) op(n,[2,3,4,5,6,1]) ; end:

%p 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:

%p seq(A165304(n),n=1..60) ; # _R. J. Mathar_, Oct 16 2009

%Y Cf. A165300-A165303, A165305-A165307.

%K easy,nonn,base

%O 1,2

%A _Paolo P. Lava_ and _Giorgio Balzarotti_, Sep 14 2009

%E Keyword:base added, sequence extended by _R. J. Mathar_, Oct 16 2009