%I #26 Apr 03 2020 07:51:10
%S 2,7,37,241,1801,15121,141121,1451521,16329601,199584001,37362124801,
%T 566658892801,9153720576001,23112569077678080001,
%U 186134520519971831808000001
%N Primes of the form (k+1)!*k/2 + 1.
%C The next term, for k = 251 (see A301373), is
%C 2566282033898537172673689833660299199318441\
%C 47812028978290091772271674111238846647249346322032725585967946013083615\
%C 44220440938904033673583084158870025082998875790404475054647299641196409\
%C 72934112662249702715026203933143550590243427364871765801696382591273000\
%C 77256511620017707120387621962694782616283336623216978502662268159966484\
%C 36506095391239127788493879085200485514817503469381297494013097308996216\
%C 58710310236069486145497777789215839354880000000000000000000000000000000\
%C 0000000000000000000000000000001
%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.
%F a(n) = A300559(A301373(n)) for all n >= 1; a(n) = A300559(n) for 1 <= n <= 10. - _M. F. Hasler_, Apr 15 2018
%t Reap[For[k = 1, k <= 1000, k++, If[PrimeQ[p = (k+1)! k/2 + 1], Print["k = ", k, " p = ", p]; Sow[p]]]][[2, 1]]
%Y Cf. A300559, A301373.
%K nonn
%O 1,1
%A _Maheswara Rao Valluri_, Apr 03 2018
%E This sequence was originally submitted as A302174, then withdrawn, then reinstated with a new A-number by _N. J. A. Sloane_, Apr 14 2018