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%I #5 Feb 23 2018 09:46:12
%S 1,4,6,7,2,12,17,20,21,14,3,8,5,9,16,15,23,18,13,11,22,19,24,10,34,26,
%T 29,36,39,32,27,35,40,31,37,38,28,30,47,42,44,33,43,48,50,49,46,51,54,
%U 41,45,52,57,25,56,58,53,65,62,55,59,60,64,61,63,66,67,68,69,70,71,74,73,75,72,76,79,82,77,84,81,80,78,83,88,85,97,86,87
%N Lexicographic first sequence of positive integers such that a(n)*a(n+1) has a digit 4, 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) = 4 is the least positive integer > a(1) = 1 such that a(2)*a(1) = 4 has a digit 4.
%e a(3) = 6 is the least positive integer not in {1, 4} such that a(3)*a(2) (= 24) has a digit 4: The smaller choices 2, 3 and 5 do not satisfy this.
%e a(4) = 7 is the least positive integer not in {1, 4, 6} such that a(4)*a(3) (= 42) has a digit 4: All available smaller choices do not satisfy this.
%o (PARI) A298974(n,f=1,d=4,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, A299403, A298975, ..., A298979: analog with digit 2, 3; ..., 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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