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

Author

Paolo P. Lava and Giorgio Balzarotti, Sep 14 2009

Keywords

• easy
• nonn
• base
• look

Comments

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

Examples

			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.
		

Links

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

Crossrefs

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

Cf. A081549 (strictly increasing version).

Programs

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 *)

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

Extensions

Edited by Charles R Greathouse IV, Aug 03 2010