A302940 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.

2, 3, 4, 5, 7, 9, 44, 47, 49, 54, 55, 57, 59, 74, 75, 77, 79, 95, 97, 99, 444, 445, 447, 449, 454, 455, 457, 459, 474, 477, 479, 494, 497, 499, 544, 545, 547, 549, 554, 555, 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

Offset: 1

Author

Jean-Marc Falcoz and Eric Angelini, Apr 16 2018

Keywords

• nonn
• base

Comments

a(1) = 0 is forbidden as [0 x a(n)] = 0, a term of the sequence;

a(1) = 1 is forbidden as [1 x a(n)] = a(n), a term of the sequence;

a(1) = 2 is ok;

a(2) = 3 is ok;

a(3) = 4 is ok, but no more digits 2 as (2 x 2) = 4;

a(4) = 5 is ok as (5 x 2), (5 x 3), (5 x 4)... are > 9;

a(5) = 6 is forbidden as (2 x 3) = 6;

a(5) = 7 is ok as (7 x 2), (7 x 3), (7 x 4)... are > 9;

a(6) = 8 is forbidden as (2 x 4) = 8;

a(6) = 9 is ok, but no more digits 3 as (3 x 3) = 9.

The other terms of the sequence use only digits 4,5,7 and 9.

Examples

			2 x 3 = 6 and there is no term or digit 6 in the sequence;
2 x 4 = 8 and there is no term or digit 8 in the sequence;
2 x 5 = 10 and there is no term 10 in the sequence;
2 x 6 = 12 and there is no term 12 in the sequence;
2 x 7 = 14 and there is no term 14 in the sequence;
2 x 9 = 18 and there is no term 18 in the sequence;
3 x 4 = 12 and there is no term 12 in the sequence;
3 x 5 = 15 and there is no term 15 in the sequence;
etc.
		

Links

• Jean-Marc Falcoz, Table of n, a(n) for n = 1..1002

Crossrefs

Cf. A302938 where the word “product” is replaced by “sum”.