A165307 Minimum number n, not already present, that permits the cyclic repetition of the decimal digits 1,2,3,4,5,6,7,8,9 in the sequence.

1, 2, 3, 4, 5, 6, 7, 8, 9, 12, 34, 56, 78, 91, 23, 45, 67, 89, 123, 456, 789, 1234, 567, 891, 234, 5678, 912, 345, 678, 9123, 4567, 8912, 3456, 7891, 2345, 6789, 12345, 67891, 23456, 78912, 34567, 89123, 45678, 91234, 56789, 123456, 789123, 456789, 1234567

Offset

1,2

Comments

This sequence has a nice graph. - M. F. Hasler, Aug 16 2015

Links

Ivan Neretin, Table of n, a(n) for n = 1..500

Example

Starting from 1,2,3,4,5,6,7,8,9 the next number is 12 because after 1,2,3,4,5,6,7,8,9 we must continue with a digit '1'. But 1 is already in the sequence so we need to append a 2, which yields 12. And so on.

Mathematica

a = {1}; c = 0; Do[c = 10 c + Mod[n, 9] + 1; If[! MemberQ[a, c], AppendTo[a, c]; c = 0], {n, 160}]; a (* Ivan Neretin, Aug 14 2015 *)

Prog

(PARI) a(n, show=0, u=[], d=[1, 1])={my(s(d)=Strchr(vectorsmall(d[1], i, (d[2]-2+i)%9+49))); while(n--, show&&print1(s(d)", "); u=setunion(u, [d]); #u>9 && u[10]==[u[1][1]+1, 1] && u=u[10..-1]; d=(d[1]+d[2]-1)%9+1; for(nd=u[1][1], 9e9, if(!setsearch(u, [nd, d]), d=[nd, d]; next(2)))); eval(s(d))} \\ M. F. Hasler, Aug 16 2015

Crossrefs

Cf. A165300, A165301, A165302, A165303, A165304, A165305, A165306.

Cf. A081549 (strictly increasing version).

Sequence in context: A290386 A290388 A302504 * A081549 A085889 A342951

Adjacent sequences: A165304 A165305 A165306 * A165308 A165309 A165310

Keyword

easy,nonn,base,look

Author

Paolo P. Lava and Giorgio Balzarotti, Sep 14 2009

Extensions

Edited by Charles R Greathouse IV, Aug 03 2010

Status

approved