A121616 Primes of form (k+1)^5 - k^5 = A022521(k).

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

Offset: 1

Author

Alexander Adamchuk, Aug 10 2006

Keywords

• nonn

Comments

Might be called "Pentan primes" (in analogy with Cuban primes, of the form (n+1)^3-n^3), or "Nexus primes of order 5" (cf. link below).

Indices k such that Nexus number of order 5 (or A022521(k-1) = k^5 - (k-1)^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.

Crossrefs

Cf. A022521, A000040, A000043, A002144, A000668, A002407, A121617, A121618, A121619, A121620.

Programs

Magma

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

Mathematica

Select[Table[n^5 - (n-1)^5, {n,1,200}],PrimeQ]
Select[Differences[Range[100]^5],PrimeQ] (* Harvey P. Dale, Nov 03 2021 *)