

A190527


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


7



31, 2801, 30941, 88741, 292561, 732541, 3500201, 28792661, 39449441, 48037081, 262209281, 1394714501, 2666986681, 3276517921, 4802611441, 5908670381, 12936304421, 16656709681, 19408913261, 24903325661, 37226181521, 43713558101, 52753304641, 64141071121, 96427561501, 100648118041
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OFFSET

1,1


COMMENTS

These primes are generated by exactly A065509.
This sequence is included in A088548.
These numbers are repunit primes 11111_n, so they are Brazilian primes belonging to A085104.
When p^4 + p^3 + p^2 + p + 1 is a prime then A193574(p^4) = sigma(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

a(n) = A193574(A065509(n)^4).  Hartmut F. W. Hoft, May 08 2017


EXAMPLE

a(3) = 30941 = 11111_13 = 13^4 + 13^3 + 13^2 + 13^1 + 1 is prime.


MATHEMATICA

a190527[n_] := Select[Map[(Prime[#]^51)/(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


CROSSREFS

Cf. A049409, A065509, A085104, A088548.
Cf. A053699, A131992, A193574.
Sequence in context: A262642 A273983 A173563 * A106205 A218424 A259866
Adjacent sequences: A190524 A190525 A190526 * A190528 A190529 A190530


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


STATUS

approved



