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A165301 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 (and repeat). 4
1, 2, 3, 12, 31, 23, 123, 1231, 231, 2312, 312, 3123, 12312, 31231, 23123, 123123, 1231231, 231231, 2312312, 312312, 3123123, 12312312, 31231231, 23123123, 123123123, 1231231231, 231231231, 2312312312, 312312312, 3123123123, 12312312312, 31231231231 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,2

LINKS

Table of n, a(n) for n=1..32.

EXAMPLE

Starting from 1, 2, 3, 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

cyc3 := proc(n) op(n, [2, 3, 1]) ; end:

A165301 := proc(n) option remember ; local k, prev, d, a ; if n = 1 then 1; else d := cyc3(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 := cyc3(d) ; a := 10*a+d ; end do; end if ; end proc:

seq(A165301(n), n=1..60) ; # R. J. Mathar, Oct 16 2009

CROSSREFS

Cf. A165300, A165302-A165307.

Sequence in context: A073617 A034381 A076424 * A072440 A135522 A107240

Adjacent sequences:  A165298 A165299 A165300 * A165302 A165303 A165304

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 May 16 08:07 EDT 2021. Contains 343940 sequences. (Running on oeis4.)