This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.
%I A165304 #6 May 05 2019 02:15:11 %S A165304 1,2,3,4,5,6,12,34,56,123,45,61,23,456,1234,561,234,5612,345,612,3456, %T A165304 12345,6123,4561,2345,61234,56123,45612,34561,23456,123456,1234561, %U A165304 234561,2345612,345612,3456123,456123,4561234,561234,5612345,612345,6123456,12345612 %N 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). %e A165304 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 A165304 cyc6 := proc(n) op(n,[2,3,4,5,6,1]) ; end: %p A165304 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 A165304 seq(A165304(n),n=1..60) ; # _R. J. Mathar_, Oct 16 2009 %Y A165304 Cf. A165300-A165303, A165305-A165307. %K A165304 easy,nonn,base %O A165304 1,2 %A A165304 _Paolo P. Lava_ and _Giorgio Balzarotti_, Sep 14 2009 %E A165304 Keyword:base added, sequence extended by _R. J. Mathar_, Oct 16 2009