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

0,1

Comments

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

Links

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

Formula

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

Example

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.

Crossrefs

Cf. A000040, A007443, A384676.

Sequence in context: A131741 A277098 A096650 * A186641 A215354 A129201

Adjacent sequences: A111104 A111105 A111106 * A111108 A111109 A111110

Keyword

easy,nonn

Author

Daniel Joyce, Oct 14 2005

Extensions

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

Status

approved