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%I #8 Feb 23 2018 09:46:28
%S 1,9,10,19,5,18,11,27,7,13,3,23,4,24,8,12,16,6,15,26,35,14,21,29,17,
%T 37,25,36,22,41,34,28,32,30,31,39,46,2,45,20,47,42,38,50,58,33,43,44,
%U 59,49,40,48,52,56,53,55,54,61,64,62,63,57,51,69,68,72,82,60,65,66,75,79,67,70,71,76,78,73,81,74,77,83,84,88,90,91,87,80,99
%N Lexicographic first sequence of positive integers such that a(n)*a(n+1) has a digit 9, 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) = 9 is the least positive integer > a(1) = 1 such that a(2)*a(1) = 9 has a digit 9.
%e a(3) = 10 is the least positive integer not in {1, 9} such that a(3)*a(2) (= 90) has a digit 9: The smaller choices 2, ..., 8 does not satisfy this.
%e a(4) = 19 is the least positive integer not in {1, 9, 10} such that a(4)*a(3) (= 190) has a digit 5: All available smaller choices do not satisfy this.
%o (PARI) A298979(n,f=1,d=9,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, A299981, A299402, A299403, A298974, A298975, A299996, A299997, A298978 : analog with digit 0, 1,..., 8.
%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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