A339613 Number of sets of distinct primes whose sum is a prime, the largest element of a set is prime(n).

1, 2, 2, 2, 5, 8, 15, 30, 57, 115, 211, 398, 783, 1528, 3002, 5893, 11432, 22247, 43663, 86348, 170472, 335636, 662988, 1312816, 2595986, 5121351, 10096635, 19930303, 39469458, 78311512, 155219706, 307373610, 607613871, 1202463562, 2383024521, 4736192475, 9413441133

Offset: 1

Author

Ilya Gutkovskiy, Dec 09 2020

Keywords

• nonn

Examples

			a(6) = 8 sets: {13}, {3, 7, 13}, {5, 11, 13}, {7, 11, 13}, {2, 3, 5, 13}, {2, 3, 11, 13}, {2, 5, 11, 13} and {2, 3, 5, 7, 11, 13}.
		

Crossrefs

Cf. A000040, A071810 (partial sums), A127542.

Programs

Python

from sympy import prime, isprime
from functools import lru_cache
@lru_cache(maxsize=None)
def b(n, s, c):
  if n == 0:
    if isprime(s): return 1
    return 0
  return b(n-1, s, c) + b(n-1, s+prime(n), c+1)
a = lambda n: b(n-1, prime(n), 1)
print([a(n) for n in range(1, 20)]) # Michael S. Branicky, Dec 10 2020

Extensions

a(35)-a(37) from Michael S. Branicky, Dec 09 2020