A320518 Zumkeller primes: k is prime and k + 1 is Zumkeller.

5, 11, 19, 23, 29, 41, 47, 53, 59, 79, 83, 89, 101, 103, 107, 113, 131, 137, 139, 149, 167, 173, 179, 191, 197, 223, 227, 233, 239, 251, 257, 263, 269, 271, 281, 293, 307, 311, 317, 347, 349, 353, 359, 367, 379, 383, 389, 401, 419, 431, 439, 443, 461, 463

Offset: 1

Author

Peter Luschny, Oct 14 2018

Keywords

• nonn

Links

• Amiram Eldar, Table of n, a(n) for n = 1..10000

Crossrefs

Cf. A083207, A000040.

Programs

Maple

isZumkellerPrime := n -> isprime(n) and isZumkeller(n+1):
A320518_list := upto -> select(isZumkellerPrime, [$1..upto]): A320518_list(500);

Mathematica

ZumkellerQ[n_] := Module[{d = Divisors[n], ds, x}, ds = Total[d]; If[OddQ[ds], False, SeriesCoefficient[Product[1 + x^i, {i, d}], {x, 0, ds/2}] > 0]];
Select[Prime[Range[100]], ZumkellerQ[# + 1]&] (* Jean-François Alcover, Mar 01 2019 *)