

A304237


a(n) is the smallest positive integer not yet in the sequence that is obtained when the first and last digits of a(n1) are exchanged and used in a(n) in the exchanged order (but not necessarily adjacent); a(1)=10.


1



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
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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



