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 A100603 Numbers k such that (prime(k)-1)! + prime(k)^4 is prime. 0
 1, 2, 4, 67, 212, 1615 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,2 COMMENTS k = {1, 2, 4, 67} yields primes p(k) = {2, 3, 7, 331}. There are no more such k up to k=100. Computed in collaboration with Ray Chandler. Terms a(5) and greater are only probable primes. - Iain Fox, Mar 05 2018 LINKS J. V. Post, Math Pages. FORMULA Numbers k such that (prime(k)-1)! + prime(k)^4 is prime, where prime(k) is the k-th prime. EXAMPLE a(3) = 4 because (prime(4)-1)! + prime(4)^4 = (7-1)! + 7^4 = 720 + 2401 = 3121 is the 3rd prime of this form. MATHEMATICA lst={}; Do[p=Prime[n]; If[PrimeQ[(p-1)!+p^4], AppendTo[lst, n]], {n, 10^2}]; lst (* Vladimir Joseph Stephan Orlovsky, Sep 08 2008 *) PROG (PARI) is(k) = my(p=prime(k)); ispseudoprime((p-1)! + p^4) \\ Iain Fox, Mar 05 2018 CROSSREFS Cf. A100858. Sequence in context: A219735 A279969 A018364 * A301818 A054920 A062061 Adjacent sequences:  A100600 A100601 A100602 * A100604 A100605 A100606 KEYWORD nonn,more AUTHOR Jonathan Vos Post, Nov 30 2004 EXTENSIONS a(5) from Iain Fox, Mar 05 2018 a(6) from Iain Fox, Mar 11 2018 STATUS approved

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Last modified June 25 03:09 EDT 2021. Contains 345449 sequences. (Running on oeis4.)