login

Year-end appeal: Please make a donation to the OEIS Foundation to support ongoing development and maintenance of the OEIS. We are now in our 61st year, we have over 378,000 sequences, and we’ve reached 11,000 citations (which often say “discovered thanks to the OEIS”).

A194257
Primes of the form p^6 + p^5 + p^4 + p^3 + p^2 + p + 1 when p is prime.
6
127, 1093, 19531, 5229043, 25646167, 917087137, 52379047267, 153436090543, 502628805631, 11016462577051, 18871143464293, 251059142817757, 1812169199976451, 1940350890330343
OFFSET
1,1
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
FORMULA
a(n) = A193574(A163268(n)^6). - Hartmut F. W. Hoft, May 08 2017
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 *)
CROSSREFS
KEYWORD
nonn
AUTHOR
Bernard Schott, Dec 21 2012
STATUS
approved