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%I #4 Feb 23 2018 09:46:41
%S 1,10,11,12,9,2,5,3,4,25,6,17,7,13,8,14,15,21,31,23,18,34,24,38,27,19,
%T 22,28,29,35,26,16,32,33,36,30,37,39,40,41,42,43,44,45,47,46,59,20,50,
%U 62,51,61,52,56,57,53,55,58,54,65,48,66,63,67,73,70,74,69,49,64,80,77,82,75,68,76,81,71,72,78,79,85,60,86,83,87,91,90,89
%N Lexicographic first sequence of positive integers such that a(n)*a(n+1) has a digit 1, and no term occurs twice.
%C A permutation of the positive integers.
%e a(1) = 1 is the least positive integer, and a(1) has no other constraint to satisfy.
%e a(2) = 10 is the least positive integer > a(1) = 1 such that a(2)*a(1) = 10 has a digit 1. (For all small choices 2, ..., 9 this is not the case.)
%e a(3) = 11 is the smallest positive integer not in {1, 10} such that a(3)*a(2) (= 110) has a digit 1.
%e a(4) = 12 is the least positive integer not in {1, 10, 11} such that a(4)*a(3) (= 132) has a digit 1: All smaller choices 2, 3, ..., 9 do not satisfy this.
%o (PARI) A299981(n,f=1,d=1,a=1,u=[a])={for(n=2,n,f&&if(f==1,print1(a","),write(f,n-1," "a)); for(k=u[1]+1,oo, setsearch(u,k)&&next;setsearch(Set(digits(a*k)),d)&&(a=k)&&break);u=setunion(u,[a]);while(#u>1&&u[2]==u[1]+1,u=u[^1]));a}
%Y Cf. A299980, A299402, A299403, A298974, A298975, A299996, A299997, A298978, A298979: analog with digit 0, 2, ..., 9.
%Y Cf. A299957, A299969, ..., A299988: analog with addition instead of multiplication, and different digits.
%K nonn,base
%O 1,2
%A _M. F. Hasler_, Feb 22 2018
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