A172034 Partial sums of Pillai primes (A063980).

23, 52, 111, 172, 239, 310, 389, 472, 581, 718, 857, 1006, 1199, 1426, 1659, 1898, 2149, 2406, 2675, 2946, 3223, 3516, 3823, 4134, 4451, 4810, 5189, 5572, 5961, 6358, 6759, 7178, 7609, 8058, 8519, 8982, 9449, 9928, 10427, 10930, 11451, 12008, 12571

Offset: 1

Author

Jonathan Vos Post, Jan 23 2010

Keywords

• nonn

Comments

The values alternate between odd and even. The first prime partial sum of Pillai primes is a(5) = 23 + 29 + 59 + 61 + 67 = 239. The second prime partial sum is a(7) = 389. The next such primes are a(11) = 857 (= the 72nd Pillai prime), a(23) = 3823, a(25) = 4451, a(27) = 5189. The coincidence which prompted this sequence is that the 266th Pillai prime is a(23), the sum of the first 23 Pillai primes. Curiously, 23 is the smallest Pillai prime. What are the next such Pillai primes in the partial sum?

Examples

			a(1) = 23 because 23 is the first Pillai prime A063980(1). a(2) = 52 because 23+29 = 52 is the sum of the first two Pillai primes A063980(1)+A063980(2).
		

Formula

a(n) = SUM[i=i..n]A063980(i) = SUM[i=i..n] {p: p prime and there exists an integer m such that m!+1 is 0 mod p and p is not 1 mod m}.

Extensions

More terms from R. J. Mathar, Jan 24 2010