A177791 Partial sums of A050705.

10, 22, 36, 51, 71, 92, 118, 151, 186, 224, 268, 316, 367, 432, 500, 586, 679, 775, 886, 998, 1114, 1237, 1398, 1586, 1787, 1990, 2196, 2405, 2615, 2830, 3051, 3329, 3626, 3926, 4230, 4536, 4857, 5209, 5565, 5936, 6320, 6715, 7113, 7526, 7946, 8387, 8858

Offset: 1

Author

Jonathan Vos Post, May 13 2010

Keywords

• nonn

Comments

Partial sums of composite number such that when sum of its prime factors is added or subtracted becomes prime. The subsequence of primes in the partial sums begins: 71, 151, 367, 1237, 1787, 3329, 5209, 8387, 9343, 13781. The subsequence of partial sums which are themselves composite number such that when sum of their prime factors is added or subtracted becomes prime, begins: 10, 51, which other such fixed points are there?

Examples

			a(13) = 10 + 12 + 14 + 15 + 20 + 21 + 26 + 33 + 35 + 38 + 44 + 48 + 51 = 367 is prime.
		

Crossrefs

Cf. A000040, A001414, A050705, A050703-A050710.

Formula

a(n) = SUM[i=1..n] A050705(i) = SUM[i=1..n] {n such that n+A001414(n) is in A000040, and n-A001414(n) is in A000040}.