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A299403 Lexicographic first sequence of positive integers such that a(n)*a(n+1) has a digit 3, and no term occurs twice.

%I A299403 #6 Feb 23 2018 09:47:22
%S A299403 1,3,10,13,11,12,25,14,17,2,15,9,4,8,29,7,5,6,22,16,19,18,20,65,21,23,
%T A299403 31,27,39,24,43,32,26,36,37,28,44,30,41,33,40,34,45,52,46,42,55,56,47,
%U A299403 49,48,57,53,51,38,35,58,54,59,60,50,61,62,63,64,68,74,72,81,66,93,67,69,70,76,71,73,84,75,85,78,82,77,79,80,92,83,86,97
%N A299403 Lexicographic first sequence of positive integers such that a(n)*a(n+1) has a digit 3, and no term occurs twice.
%C A299403 A permutation of the positive integers.
%e A299403 a(1) = 1 is the least positive integer, and a(1) has no other constraint to satisfy.
%e A299403 a(2) = 3 is the least positive integer > a(1) = 1 such that a(2)*a(1) = 3 has a digit 3.
%e A299403 a(3) = 10 is the least positive integer not in {1, 3} such that a(3)*a(2) (= 30) has a digit 3: All smaller choices 2, 4, ..., 9 do not satisfy this.
%e A299403 a(4) = 13 is the least positive integer not in {1, 3, 10} such that a(4)*a(3) (= 130) has a digit 3: All smaller choices do not satisfy this.
%o A299403 (PARI) A299403(n,f=1,d=3,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 A299403 Cf. A299402, A298974, ..., A298979: analog with digit 2, 3; ..., 9.
%Y A299403 Cf. A299957, A299969, ..., A299988 (analog with addition instead of multiplication, and different digits).
%K A299403 nonn,base
%O A299403 1,2
%A A299403 _M. F. Hasler_, Feb 22 2018