OFFSET
1,1
COMMENTS
These primes are generated by exactly A065509, cf. 2nd formula.
These numbers are repunit primes 11111_p, so they are Brazilian primes (A085104).
When p^4 + p^3 + p^2 + p + 1 = sigma(p^4) is prime, then it equals A193574(p^4), so that this sequence is a subsequence of A193574; by definition it is also a subsequence of A053699 and A131992. - Hartmut F. W. Hoft, May 05 2017
LINKS
Vincenzo Librandi, Table of n, a(n) for n = 1..1100
FORMULA
EXAMPLE
a(3) = 30941 = 11111_13 = 13^4 + 13^3 + 13^2 + 13^1 + 1 is prime.
MATHEMATICA
a190527[n_] := Select[Map[(Prime[#]^5-1)/(Prime[#]-1)&, Range[n]], PrimeQ]
a190527[100] (* data *) (* Hartmut F. W. Hoft, May 05 2017 *)
Select[#^4 + #^3 + #^2 + # + 1 &/@Prime[Range[100]], PrimeQ] (* Vincenzo Librandi, May 06 2017 *)
PROG
(Magma)[p: p in PrimesUpTo(600) | IsPrime(p) where p is p^4 +p^3+p^2+p+1]; // Vincenzo Librandi, May 06 2017
(PARI)
[q|p<-primes(100), ispseudoprime(q=(p^5-1)\(p-1))]
CROSSREFS
KEYWORD
nonn
AUTHOR
Bernard Schott, Dec 20 2012
EXTENSIONS
a(7) corrected and a(18)-a(26) added by Hartmut F. W. Hoft, May 05 2017
Edited by M. F. Hasler, Mar 06 2020
STATUS
approved