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 A100289 Numbers k such that (1!)^2 + (2!)^2 + (3!)^2 + ... + (k!)^2 is prime. 8
 2, 3, 4, 5, 7, 8, 10, 18, 21, 42, 51, 91, 133, 177, 182, 310, 3175, 9566, 32841 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,1 COMMENTS All k <= 310 yield provable primes. Write the sum as S(2,k)-1, where S(m,k) = Sum_{i=0..k} (i!)^m. Let p=1248829. Because p divides S(2,p-1)-1, p divides S(2,k)-1 for all k >= p-1. Hence there are no primes for k >= p-1. LINKS Table of n, a(n) for n=1..19. Eric Weisstein's World of Mathematics, Factorial Sums Eric Weisstein's World of Mathematics, Integer Sequence Primes MAPLE L:= [seq((i!)^2, i=1..1000)]: S:= ListTools:-PartialSums(L): select(t -> isprime(S[t]), [\$1..1000]); # Robert Israel, Jul 17 2017 MATHEMATICA Select[Range[200], PrimeQ[Total[Range[#]!^2]] &] PROG (PARI) is(n)=ispseudoprime(sum(k=1, n, k!^2)) \\ Charles R Greathouse IV, Apr 14 2015 CROSSREFS Cf. A100288 (primes of the form (1!)^2 + (2!)^2 + (3!)^2 +...+ (k!)^2). Cf. A061062 ((0!)^2 + (1!)^2 + (2!)^2 + (3!)^2 +...+ (n!)^2). Cf. A289947 (k!^6), A290014 (k!^10). Cf. also A104344. Sequence in context: A034296 A075745 A214036 * A255130 A054021 A066191 Adjacent sequences: A100286 A100287 A100288 * A100290 A100291 A100292 KEYWORD nonn,fini,more AUTHOR T. D. Noe, Nov 11 2004 and Dec 11 2004 EXTENSIONS a(18) from T. D. Noe, Feb 15 2006 a(19) from Serge Batalov, Jul 29 2017 STATUS approved

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Last modified September 27 11:23 EDT 2023. Contains 365688 sequences. (Running on oeis4.)