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 A100289 Numbers n such that (1!)^2 + (2!)^2 + (3!)^2 +...+ (n!)^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 n <= 310 yield provable primes. Write the sum as S(2,n)-1, where S(k,n) = sum_{i=0..n} (i!)^k. Let p=1248829. Because p divides S(2,p-1)-1, p divides S(2,n)-1 for all n >= p-1. Hence there are no primes for n >= p-1. LINKS 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 AUTHOR T. D. Noe, Nov 11 2004 and Dec 11 2004 EXTENSIONS a(18) from T. D. Noe, Feb 15 2006 a(19) = 32841 from Serge Batalov, Jul 29 2017 STATUS approved

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Last modified December 12 01:57 EST 2019. Contains 329948 sequences. (Running on oeis4.)