A302859 Primes of the form (k+1)!*k/2 + 1.

2, 7, 37, 241, 1801, 15121, 141121, 1451521, 16329601, 199584001, 37362124801, 566658892801, 9153720576001, 23112569077678080001, 186134520519971831808000001

Offset: 1

Author

Maheswara Rao Valluri, Apr 03 2018

Keywords

• nonn

Comments

The next term, for k = 251 (see A301373), is

2566282033898537172673689833660299199318441\

47812028978290091772271674111238846647249346322032725585967946013083615\

44220440938904033673583084158870025082998875790404475054647299641196409\

72934112662249702715026203933143550590243427364871765801696382591273000\

77256511620017707120387621962694782616283336623216978502662268159966484\

36506095391239127788493879085200485514817503469381297494013097308996216\

58710310236069486145497777789215839354880000000000000000000000000000000\

0000000000000000000000000000001

Links

• Maheswara Rao Valluri, Primes of the form p = 1 + n! Sum n, for some n ∈ N*, arXiv:1803.11461 [math.GM], 2018.

Crossrefs

Cf. A300559, A301373.

Programs

Mathematica

Reap[For[k = 1, k <= 1000, k++, If[PrimeQ[p = (k+1)! k/2 + 1], Print["k = ", k, " p = ", p]; Sow[p]]]][[2, 1]]

Formula

a(n) = A300559(A301373(n)) for all n >= 1; a(n) = A300559(n) for 1 <= n <= 10. - M. F. Hasler, Apr 15 2018

Extensions

This sequence was originally submitted as A302174, then withdrawn, then reinstated with a new A-number by N. J. A. Sloane, Apr 14 2018