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

1,1

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?

Links

Table of n, a(n) for n=1..47.

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}.

Example

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.

Sequence in context: A217573 A276626 A211482 * A028569 A014367 A063710

Adjacent sequences: A177788 A177789 A177790 * A177792 A177793 A177794

Keyword

nonn

Author

Jonathan Vos Post, May 13 2010

Status

approved