A194257 Primes of the form p^6 + p^5 + p^4 + p^3 + p^2 + p + 1 when p is prime.

127, 1093, 19531, 5229043, 25646167, 917087137, 52379047267, 153436090543, 502628805631, 11016462577051, 18871143464293, 251059142817757, 1812169199976451, 1940350890330343

Offset: 1

Author

Bernard Schott, Dec 21 2012

Keywords

• nonn

Comments

These primes are generated by exactly A163268.

This sequence is included in A088550.

These numbers are repunit primes 1111111_n, so they are Brazilian primes and are terms of A085104.

Subsequence of A088550. - Hartmut F. W. Hoft, May 05 2017

Links

• Robert Israel, Table of n, a(n) for n = 1..10000

Crossrefs

Cf. A085104, A088550, A100330, A163268.

Programs

Maple

select(isprime, map(p -> add(p^i,i=0..6), select(isprime, [2,seq(i,i=3..1000,2)]))); # Robert Israel, May 05 2017

Mathematica

a194257[n_] := Select[Map[(Prime[#]^7-1)/(Prime[#]-1)&, Range[n]], PrimeQ]
a194257[70] (* data *) (* Hartmut F. W. Hoft, May 05 2017 *)
Select[Table[Total[p^Range[0,6]],{p,Prime[Range[100]]}],PrimeQ] (* Harvey P. Dale, Mar 09 2024 *)

Formula

a(n) = A193574(A163268(n)^6). - Hartmut F. W. Hoft, May 08 2017