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 A114337 Primes which are 1/3 of the cumulative sum of factorials of primes, if 1 is used as the zeroth prime. 1
 3, 43, 1723, 13307323 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,1 COMMENTS No more primes. Starting with a(14) = (1! + ... + 43!)/3 the sum always has a factor of 47. LINKS FORMULA Defining prime(0)= 1: a(n) = (1/3)*Sum_{i=0..n}A000142(A000040(i+1)) iff in A000040. a(n) = (1/3)*Sum_{i=0..n}prime(i+1)! iff in A000040. EXAMPLE prime(0)! = 1! = 1; prime(1)! = 2! = 2. a(1) = (1! + 2! + 3!)/3 = 9/3 = 3. a(2) = (1! + 2! + 3! + 5!)/3 = 129/3 = 43. a(3) = (1! + 2! + 3! + 5! + 7!)/3 = 5169/3 = 1723. a(4) = (1! + 2! + 3! + 5! + 7! + 11!)/3 = 39921969/3 = 13307323. MATHEMATICA f[n_] := (1 + Plus @@ ((Prime@ Range@ n)!))/3; Select[f /@ Range@ 43, PrimeQ@# &] (* Robert G. Wilson v, Apr 30 2009 *) CROSSREFS Cf. A000040, A000142. Sequence in context: A274387 A300988 A136648 * A317343 A307248 A009720 Adjacent sequences:  A114334 A114335 A114336 * A114338 A114339 A114340 KEYWORD fini,full,nonn AUTHOR Jonathan Vos Post, Feb 07 2006 STATUS approved

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Last modified April 16 04:49 EDT 2021. Contains 343030 sequences. (Running on oeis4.)