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 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). 4
 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 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,2 LINKS 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: A236371 A173446 A053350 * A276530 A251411 A117342 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

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Last modified October 14 18:28 EDT 2019. Contains 328022 sequences. (Running on oeis4.)