editing

approved

seq(A165304(n), n=1..60) ; # _R. J. Mathar, _, Oct 16 2009

Cf. A165300-A165303, A165305-A165307.

approved

editing

_Paolo P. Lava & _ and _Giorgio Balzarotti (paoloplava(AT)gmail.com), _, Sep 14 2009

Keyword:base added, sequence extended by _R. J. Mathar (mathar(AT)strw.leidenuniv.nl), _, Oct 16 2009

Paolo P. Lava & Giorgio Balzarotti (pplpaoloplava(AT)splgmail.atcom), Sep 14 2009

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

1,2

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.

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

A165300-A165303, A165305-A165307

easy,nonn,base

Paolo P. Lava & Giorgio Balzarotti (ppl(AT)spl.at), Sep 14 2009

Keyword:base added, sequence extended by R. J. Mathar (mathar(AT)strw.leidenuniv.nl), Oct 16 2009

approved