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

1,1

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.

Links

Table of n, a(n) for n=1..65.

Example

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).

Prog

(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

Crossrefs

Cf. A107353, A303605.

Sequence in context: A139103 A067217 A266175 * A304238 A231889 A066327

Adjacent sequences: A304234 A304235 A304236 * A304238 A304239 A304240

Keyword

nonn,base

Author

Enrique Navarrete, May 08 2018

Status

approved