cp's OEIS Frontend

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

%I A339613 #11 Dec 10 2020 08:52:50
%S A339613 1,2,2,2,5,8,15,30,57,115,211,398,783,1528,3002,5893,11432,22247,
%T A339613 43663,86348,170472,335636,662988,1312816,2595986,5121351,10096635,
%U A339613 19930303,39469458,78311512,155219706,307373610,607613871,1202463562,2383024521,4736192475,9413441133
%N A339613 Number of sets of distinct primes whose sum is a prime, the largest element of a set is prime(n).
%e A339613 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}.
%o A339613 (Python)
%o A339613 from sympy import prime, isprime
%o A339613 from functools import lru_cache
%o A339613 @lru_cache(maxsize=None)
%o A339613 def b(n, s, c):
%o A339613   if n == 0:
%o A339613     if isprime(s): return 1
%o A339613     return 0
%o A339613   return b(n-1, s, c) + b(n-1, s+prime(n), c+1)
%o A339613 a = lambda n: b(n-1, prime(n), 1)
%o A339613 print([a(n) for n in range(1, 20)]) # _Michael S. Branicky_, Dec 10 2020
%Y A339613 Cf. A000040, A071810 (partial sums), A127542.
%K A339613 nonn
%O A339613 1,2
%A A339613 _Ilya Gutkovskiy_, Dec 09 2020
%E A339613 a(35)-a(37) from _Michael S. Branicky_, Dec 09 2020