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A172034 Partial sums of Pillai primes (A063980). 0
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 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,1

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?

LINKS

Table of n, a(n) for n=1..43.

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}.

EXAMPLE

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).

CROSSREFS

Sequence in context: A165432 A067625 A140689 * A113912 A055782 A104802

Adjacent sequences:  A172031 A172032 A172033 * A172035 A172036 A172037

KEYWORD

nonn

AUTHOR

Jonathan Vos Post, Jan 23 2010

EXTENSIONS

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

STATUS

approved

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Last modified October 2 10:33 EDT 2014. Contains 247538 sequences.