A304237 a(n) is the smallest positive integer not yet in the sequence that is obtained when the first and last digits of a(n-1) are exchanged and used in a(n) in the exchanged order (but not necessarily adjacent); a(1)=10.

10, 101, 11, 110, 201, 12, 21, 102, 121, 111, 112, 210, 202, 22, 122, 211, 120, 301, 13, 31, 103, 131, 113, 231, 123, 310, 203, 32, 23, 132, 212, 220, 302, 213, 232, 221, 124, 41, 14, 141, 114, 241, 125, 51, 15, 151, 115, 251, 126, 61, 16, 161, 116, 261, 127, 71, 17, 171, 117, 271, 128, 81, 18, 181, 118

Offset: 1

Author

Enrique Navarrete, May 08 2018

Keywords

• nonn
• base

Comments

Up to n=82, the only consecutive numbers in the sequence are 111, 112 and 222, 223.

Could have started sequence with offset a(0)=0 and it would be the same sequence.

Examples

			a(2)=101 since 101 is the smallest positive number not yet in the sequence that is obtained when the first and last digits of a(1)=10 are exchanged and used in that order.
a(8)=102 since 102 is the smallest positive number not yet in the sequence that is obtained when the first and last digits of a(7)=21 are exchanged and used in that order (but not necessarily adjacent).
		

Crossrefs

Cf. A107353, A303605.

Programs

PARI

firstTerms(n)={my(Seq=vector(n),a=[1,0],c,y,k,h=Vecsmall(0,1000*n));print1("10,");Seq[1]=10;h[11]=1;for(i=2,n,for(t=11,oo,if(!h[t+1],c=digits(t);y=1;while((y<#c)&&(!c[y]),y++);forvec(u=[[y,#c],[y,#c]],if(k=([c[u[1]],c[u[2]]]==[a[#a],a[1]]),break),2);if(k,Seq[i]=t;print1(t",");a=c;h[t+1]=1;break))));return(Seq)} \\ R. J. Cano, May 11 2018