

A121616


Primes of form (k+1)^5  k^5 = A022521(k).


11



31, 211, 4651, 61051, 371281, 723901, 1803001, 2861461, 4329151, 4925281, 7086451, 7944301, 14835031, 19611901, 23382031, 44119351, 54664711, 86548801, 97792531, 162478501, 189882031, 267217051, 293109961, 306740281, 490099501
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OFFSET

1,1


COMMENTS

Might be called "Pentan primes" (in analogy with Cuban primes, of the form (n+1)^3n^3), or "Nexus primes of order 5" (cf. link below).
Indices k such that Nexus number of order 5 (or A022521(k1) = k^5  (k1)^5) is prime are listed in A121617 = {2, 3, 6, 11, 17, 20, 25, 28, 31, 32, 35, 36, 42, 45, 47, 55, 58, 65, 67, 76, 79, 86, 88, 89, 100,...}.
The last digit is always 1 because 5 is the Pythagorean prime A002144(1). a(1) = 31 is the Mersenne prime A000668(3).


LINKS

Zak Seidov, Table of n, a(n) for n = 1..2000.


MATHEMATICA

Select[Table[n^5  (n1)^5, {n, 1, 200}], PrimeQ]


PROG

(MAGMA) [a: n in [0..110]  IsPrime(a) where a is (n+1)^5n^5]; // Vincenzo Librandi, Jan 20 2020


CROSSREFS

Cf. A022521, A000040, A000043, A002144, A000668, A002407, A121617, A121618, A121619, A121620.
Sequence in context: A090027 A164784 A290008 * A284899 A062393 A183792
Adjacent sequences: A121613 A121614 A121615 * A121617 A121618 A121619


KEYWORD

nonn


AUTHOR

Alexander Adamchuk, Aug 10 2006


STATUS

approved



