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 A305738 Numbers k such that k!*T(k) - 1 is prime, where T(k) is the k-th triangular number. 1

%I

%S 2,4,28,34,47,62,228,256,258,341,848,1362,1709,2262,2692,7907,10396,

%T 10501

%N Numbers k such that k!*T(k) - 1 is prime, where T(k) is the k-th triangular number.

%C The PFGW program has been used to certify all the terms up to a(18), using a deterministic test which exploits the factorization of a(n) + 1. - _Giovanni Resta_, Jun 24 2018

%H Maheswara Rao Valluri, <a href="https://arxiv.org/abs/1803.11461">Primes of the form p = 1 + n! Sum n, for some n ∈ N*</a>, arXiv:1803.11461 [math.GM], 2018.

%t Do[If[ PrimeQ[n(n +1)!/2 - 1], Print@ n], {n, 3000}]

%o (PARI) isok(n) = ispseudoprime(n(n+1)!/ 2 - 1);

%Y Cf. A302859, A301373.

%K nonn,more

%O 1,1

%A _Maheswara Rao Valluri_, Jun 22 2018

%E a(16)-a(18) from _Giovanni Resta_, Jun 24 2018

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Last modified April 21 11:02 EDT 2021. Contains 343150 sequences. (Running on oeis4.)