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

1,2

Links

Table of n, a(n) for n=1..37.

Example

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}.

Prog

(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

Crossrefs

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

Sequence in context: A039886 A367087 A109523 * A008295 A216694 A116697

Adjacent sequences: A339610 A339611 A339612 * A339614 A339615 A339616

Keyword

nonn

Author

Ilya Gutkovskiy, Dec 09 2020

Extensions

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

Status

approved