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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). 4
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 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,2

LINKS

Table of n, a(n) for n=1..43.

EXAMPLE

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.

MAPLE

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

CROSSREFS

Cf. A165300-A165303, A165305-A165307.

Sequence in context: A059460 A125141 A282505 * A266642 A245450 A115307

Adjacent sequences:  A165301 A165302 A165303 * A165305 A165306 A165307

KEYWORD

easy,nonn,base

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 February 29 05:25 EST 2020. Contains 332353 sequences. (Running on oeis4.)