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%I #8 Apr 18 2018 19:57:36
%S 2,3,4,5,7,9,44,47,49,54,55,57,59,74,75,77,79,95,97,99,444,445,447,
%T 449,454,455,457,459,474,477,479,494,497,499,544,545,547,549,554,555,
%U 557,559,574,575,577,579,594,595,597,599,744,745,747,749,754,755,757,759,774,775,777,779,794,795,797,799
%N Lexicographically first sequence of distinct terms such that the product of any two terms is not a term of the sequence, and the product of any two digits is not a digit of the sequence.
%C a(1) = 0 is forbidden as [0 x a(n)] = 0, a term of the sequence;
%C a(1) = 1 is forbidden as [1 x a(n)] = a(n), a term of the sequence;
%C a(1) = 2 is ok;
%C a(2) = 3 is ok;
%C a(3) = 4 is ok, but no more digits 2 as (2 x 2) = 4;
%C a(4) = 5 is ok as (5 x 2), (5 x 3), (5 x 4)... are > 9;
%C a(5) = 6 is forbidden as (2 x 3) = 6;
%C a(5) = 7 is ok as (7 x 2), (7 x 3), (7 x 4)... are > 9;
%C a(6) = 8 is forbidden as (2 x 4) = 8;
%C a(6) = 9 is ok, but no more digits 3 as (3 x 3) = 9.
%C The other terms of the sequence use only digits 4,5,7 and 9.
%H Jean-Marc Falcoz, <a href="/A302940/b302940.txt">Table of n, a(n) for n = 1..1002</a>
%e 2 x 3 = 6 and there is no term or digit 6 in the sequence;
%e 2 x 4 = 8 and there is no term or digit 8 in the sequence;
%e 2 x 5 = 10 and there is no term 10 in the sequence;
%e 2 x 6 = 12 and there is no term 12 in the sequence;
%e 2 x 7 = 14 and there is no term 14 in the sequence;
%e 2 x 9 = 18 and there is no term 18 in the sequence;
%e 3 x 4 = 12 and there is no term 12 in the sequence;
%e 3 x 5 = 15 and there is no term 15 in the sequence;
%e etc.
%Y Cf. A302938 where the word “product” is replaced by “sum”.
%K nonn,base
%O 1,1
%A _Jean-Marc Falcoz_ and _Eric Angelini_, Apr 16 2018
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