%I #4 Feb 23 2018 09:46:20
%S 1,8,6,3,16,5,17,4,2,9,12,7,14,13,22,19,15,32,24,20,29,27,18,10,28,11,
%T 26,23,21,38,31,35,25,33,36,30,46,40,37,34,42,39,47,44,41,45,53,54,52,
%U 49,58,48,51,55,56,43,60,63,61,62,59,65,69,70,64,57,50,76,68,66,71,73,67,72,74,77,79,82,83,86,78,75,91,80,81,84,87,90,89
%N Lexicographic first sequence of positive integers such that a(n)*a(n+1) has a digit 8, 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) = 8 is the least positive integer > a(1) = 1 such that a(2)*a(1) = 8 has a digit 3.
%e a(3) = 6 is the least positive integer not in {1, 8} such that a(3)*a(2) (= 48) has a digit 8: All smaller choices 2, 4, ..., 7 do not satisfy this.
%e a(4) = 3 is the least positive integer not in {1, 6, 8} such that a(4)*a(3) (= 18) has a digit 8: The only smaller choice 2 does not satisfy this.
%o (PARI) A298978(n,f=1,d=8,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. A299402, A298974, ..., A298979: analog with digit 2, 4, ..., 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