A100595 -id:A100595 - cp's OEIS frontend

A100598 Numbers k such that (prime(k)-1)! + prime(k)^8 is prime.

1, 2, 4, 5, 8, 10

Offset: 1

Jonathan Vos Post, Nov 30 2004

k = {1, 2, 4, 5, 8, 10} yields primes p(k) = {2, 3, 7, 11, 19, 29}. There are no more such k up to k=100. Computed in collaboration with Ray Chandler.
a(7) > 600. - Jinyuan Wang, Apr 10 2020
a(7) > 900. - Tyler NeSmith, May 05 2021
a(7) > 2500. - Michael S. Branicky, Jul 03 2024

			a(1) = 1 because (prime(1)-1)! + prime(1)^8 = (2-1)! + 2^8 = 257 is the smallest prime of that form.
a(5) = 8 because (prime(8)-1)! + prime(8)^8 = (19-1)! + 19^8 = 304888344611713861001750412961 is the 5th smallest prime of that form.

Cf. A100595, A100599, A100858.

lst={};Do[p=Prime[n];If[PrimeQ[(p-1)!+p^8], AppendTo[lst, n]], {n, 10^2}];lst (* Vladimir Joseph Stephan Orlovsky, Sep 08 2008 *)

is(k) = ispseudoprime((prime(k)-1)! + prime(k)^8); \\ Jinyuan Wang, Apr 10 2020

Edited by N. J. A. Sloane at the suggestion of Andrew S. Plewe, Jun 08 2007

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

Original entry on oeis.org

2, 8, 15, 33, 52, 205, 751

Offset: 1

Jonathan Vos Post, Nov 30 2004

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.
a(7) > 600. - Jinyuan Wang, Apr 10 2020
a(8) > 2700. - Michael S. Branicky, Jul 03 2024

			a(1) = 2 because (prime(2)-1)! + prime(2)^10 = (3-1)! + 3^10 = 59051 is the smallest prime of that form.
a(2) = 8 because (prime(8)-1)! + prime(8)^10 = (19-1)! + 19^10 = 6408504771985801 is the 2nd smallest prime of that form.

Cf. A100595, A100858.

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 *)
Select[Range[250],PrimeQ[(Prime[#]-1)!+Prime[#]^10]&] (* The program generates the first 6 terms of the sequence. *) (* Harvey P. Dale, Dec 27 2024 *)

from math import factorial
from sympy import isprime, prime
def afind(limit, startat=1):
    for k in range(startat, limit+1):
        s = str(k)
        pk = prime(k)
        if isprime( factorial(pk-1) + pk**10 ):
            print(k, end=", ")
afind(100) # Michael S. Branicky, Nov 30 2021

Primes of the form (prime(k)-1)! + prime(k)^10, where prime(k) is the k-th prime.

a(6) from Jinyuan Wang, Apr 10 2020

a(7) from Michael S. Branicky, Nov 30 2021

cp's OEIS Frontend

A100598 Numbers k such that (prime(k)-1)! + prime(k)^8 is prime.

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