A111107 Lexicographically smallest increasing sequence of primes whose binomial transform consists only of primes.

2, 3, 5, 11, 13, 29, 43, 53, 59, 71, 79, 83, 103, 113, 139, 173, 181, 227, 269, 277, 317, 383, 463, 509, 673, 701, 751, 863, 967, 977, 1187, 1201, 1493, 1531, 1609, 1637, 1801, 2153, 2221, 2239, 2371, 2377, 2543, 2557, 2683, 2687, 2791, 2837, 3067, 3229, 3257

Offset: 0

Author

Daniel Joyce, Oct 14 2005

Keywords

• easy
• nonn

Comments

In the standard binomial transform of the primes most of the terms are composite.

Examples

			The binomial transform of this sequence gives: 2, 5, 13, 37, 101, 271, 727, 1931, 5003, 12547, 30449, 71761, ... = A384676.
The prime 7 and various larger primes are missing from the new sequence because the transform would not consist of primes. For example,
  2,5,13,33
  3,8,20
  5,12
  7
and 33 is not prime, so we must eliminate 7.
		

Links

• Alois P. Heinz, Table of n, a(n) for n = 0..2000

Crossrefs

Cf. A000040, A007443, A384676.

Formula

a(n) = Sum_{i=0..n} A384676(n-i)*binomial(n,i)*(-1)^i. - Alois P. Heinz, Jun 06 2025

Extensions

Offset set to 0 by Alois P. Heinz, Jun 06 2025