cp's OEIS Frontend

A100596 Numbers k such that (prime(k)-1)! + prime(k)^10 is prime.

%I A100596 #21 Dec 27 2024 13:49:33
%S A100596 2,8,15,33,52,205,751
%N A100596 Numbers k such that (prime(k)-1)! + prime(k)^10 is prime.
%C A100596 k = {2, 8, 15, 33, 52, 205} yields primes p(k) = {3, 19, 47, 137, 239, 1259}. There are no more such k up to k=150. Computed in collaboration with _Ray Chandler_.
%C A100596 a(7) > 600. - _Jinyuan Wang_, Apr 10 2020
%C A100596 a(8) > 2700. - _Michael S. Branicky_, Jul 03 2024
%F A100596 Primes of the form (prime(k)-1)! + prime(k)^10, where prime(k) is the k-th prime.
%e A100596 a(1) = 2 because (prime(2)-1)! + prime(2)^10 = (3-1)! + 3^10 = 59051 is the smallest prime of that form.
%e A100596 a(2) = 8 because (prime(8)-1)! + prime(8)^10 = (19-1)! + 19^10 = 6408504771985801 is the 2nd smallest prime of that form.
%t A100596 lst={};Do[p=Prime[n];If[PrimeQ[(p-1)!+p^10], AppendTo[lst, n]], {n, 10^2}];lst (* _Vladimir Joseph Stephan Orlovsky_, Sep 08 2008 *)
%t A100596 Select[Range[250],PrimeQ[(Prime[#]-1)!+Prime[#]^10]&] (* The program generates the first 6 terms of the sequence. *) (* _Harvey P. Dale_, Dec 27 2024 *)
%o A100596 (Python)
%o A100596 from math import factorial
%o A100596 from sympy import isprime, prime
%o A100596 def afind(limit, startat=1):
%o A100596     for k in range(startat, limit+1):
%o A100596         s = str(k)
%o A100596         pk = prime(k)
%o A100596         if isprime( factorial(pk-1) + pk**10 ):
%o A100596             print(k, end=", ")
%o A100596 afind(100) # _Michael S. Branicky_, Nov 30 2021
%Y A100596 Cf. A100595, A100858.
%K A100596 nonn,hard,more
%O A100596 1,1
%A A100596 _Jonathan Vos Post_, Nov 30 2004
%E A100596 a(6) from _Jinyuan Wang_, Apr 10 2020
%E A100596 a(7) from _Michael S. Branicky_, Nov 30 2021