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
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
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
Comments