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

1,1

Comments

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

a(1) = 1 is forbidden as [1 * 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 * 2) = 4;

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

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

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

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

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

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

Links

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

Example

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

Crossrefs

Cf. A302938 where the word "product" is replaced by "sum".

Sequence in context: A261170 A051453 A357166 * A272072 A118463 A214652

Adjacent sequences: A302937 A302938 A302939 * A302941 A302942 A302943

Keyword

nonn,base

Author

Jean-Marc Falcoz and Eric Angelini, Apr 16 2018

Status

approved