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Odd primes p that divide 2! + 3! + ... + (p-1)!.
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%I #20 Jan 21 2023 02:43:44

%S 31,373,6855730873

%N Odd primes p that divide 2! + 3! + ... + (p-1)!.

%C In other words, the odd primes p that divide A003422(p) - 2. Or the primes p with A049782(p) = 2.

%C Andrejic and Tatarevic found a(3).

%H Vladica Andrejic and Milos Tatarevic, <a href="http://arxiv.org/abs/1409.0800">Searching for a counterexample of Kurepa's Conjecture</a>, arXiv:1409.0800 [math.NT], 2014.

%o (PARI) forprime(p=3, 1e11, if(sum(k=2, p-1, k!) % p==0, print1(p, ", "))); \\ _Altug Alkan_, Nov 08 2015

%Y Cf. A003422, A049782, A100612.

%K nonn,hard,more

%O 1,1

%A _Jeppe Stig Nielsen_, Nov 07 2015