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 A248872 Numbers n such that n^n + n! + 1 is prime. 0
 1, 2, 4, 28, 496 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,2 COMMENTS These primes are of the form: A000312(n) + A000142(n) + 1. Note that 28 and 496 are perfect numbers (see A000396). a(6) > 1500. LINKS EXAMPLE For n = 1, 1^1 + 1! + 1 = 3, which is prime. For n = 2, 2^2 + 2! + 1 = 4 + 2 + 1 = 7, which is prime. For n = 4, 4^4 + 4! + 1 = 281, which is prime. MATHEMATICA Select[Range[1500], PrimeQ[#^# + #! + 1]&] PROG (PARI) for(n=1, 10^3, if(ispseudoprime(n^n+n!+1), print1(n, ", "))) \\ Derek Orr, Mar 06 2015 CROSSREFS Cf. A000312 (n^n), A000142(n!). Sequence in context: A062792 A102692 A292184 * A329102 A126580 A329063 Adjacent sequences:  A248869 A248870 A248871 * A248873 A248874 A248875 KEYWORD nonn,more,hard AUTHOR Waldemar Puszkarz, Mar 04 2015 STATUS approved

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Last modified January 23 16:44 EST 2020. Contains 331172 sequences. (Running on oeis4.)