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A165306 a(n) is the smallest number not yet in the sequence such that concatenation of all terms yields an infinite periodic stream of digits 1, 2, 3, ..., 8 (repeat from 1). 3
1, 2, 3, 4, 5, 6, 7, 8, 12, 34, 56, 78, 123, 45, 67, 81, 23, 456, 781, 234, 567, 812, 345, 678, 1234, 5678, 12345, 6781, 2345, 67812, 3456, 7812, 34567, 8123, 4567, 81234, 56781, 23456, 78123, 45678, 123456, 781234, 567812, 345678, 1234567, 812345 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,2

LINKS

Table of n, a(n) for n=1..46.

EXAMPLE

Considering a(9), having already 1,2,3,4,5,6,7,8, the next number must be 12 because after 1,2,3,4,5,6,7,8 we shall continue with a 1.

But 1 is already in the sequence so we need to add a 2 -> 12. And so on.

MAPLE

cyc8 := proc(n) op(n, [2, 3, 4, 5, 6, 7, 8, 1]) ; end:

A165306 := proc(n) option remember ; local k, prev, d, a ; if n = 1 then 1; else d := cyc8(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 := cyc8(d) ; a := 10*a+d ; end do; end if ; end proc:

seq(A165306(n), n=1..60) ; # R. J. Mathar, Feb 02 2010

CROSSREFS

Cf. A165300-A165305, A165307.

Sequence in context: A084589 A271831 A180628 * A254116 A254115 A032986

Adjacent sequences:  A165303 A165304 A165305 * A165307 A165308 A165309

KEYWORD

easy,nonn,base

AUTHOR

Paolo P. Lava and Giorgio Balzarotti, Sep 14 2009

EXTENSIONS

Keyword base added by R. J. Mathar, Feb 02 2010

STATUS

approved

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Last modified August 13 10:40 EDT 2022. Contains 356080 sequences. (Running on oeis4.)