A109860 Triangle whose n-th row contains the next n numbers relatively prime to n! and not occurring in a previous row. a(1) = 1.

1, 3, 5, 7, 11, 13, 17, 19, 23, 25, 29, 31, 37, 41, 43, 47, 49, 53, 59, 61, 67, 71, 73, 79, 83, 89, 97, 101, 103, 107, 109, 113, 121, 127, 131, 137, 139, 143, 149, 151, 157, 163, 167, 169, 173, 179, 181, 187, 191, 193, 197, 199, 209, 211, 221, 223, 227, 229, 233, 239

Offset

0,2

Comments

1

3 5

7 11 13

17 19 23 25

29 31 37 41 43

47 49 53 59 61 67

71 73 79 83 89 97 101

...

2 is the only prime that is not a member. Conjecture: There are finitely many composite terms.

The sequence contains infinitely many composites. Through n rows, there are ~ n^2/2 terms. The number of primes up to (n+1)^2 is ~ n^2/(2 log n), which is eventually quite a bit less. Most products of two nearby primes will be in the sequence. - Franklin T. Adams-Watters, Apr 14 2006

Links

Table of n, a(n) for n=0..59.

Crossrefs

Cf. A109861.

Sequence in context: A355821 A332075 A122089 * A100392 A309203 A176847

Adjacent sequences: A109857 A109858 A109859 * A109861 A109862 A109863

Keyword

nonn,tabl

Author

Amarnath Murthy, Jul 08 2005

Extensions

Corrected, extended and edited by Franklin T. Adams-Watters, Apr 14 2006

Status

approved