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%I #6 May 05 2019 02:14:28
%S 1,2,3,4,12,34,123,41,23,412,341,234,1234,12341,2341,23412,3412,34123,
%T 4123,41234,123412,341234,1234123,412341,234123,4123412,3412341,
%U 2341234,12341234,123412341,23412341,234123412,34123412,341234123,41234123,412341234
%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 (and repeat).
%e 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.
%p cyc4 := proc(n) op(n,[2,3,4,1]) ; end:
%p 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:
%p seq(A165302(n),n=1..60) ; # _R. J. Mathar_, Oct 16 2009
%Y Cf. A165300, A165301, A165303-A165307.
%K easy,base,nonn
%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
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