A363751 Numbers k such that prime(k) mod k is prime.

3, 4, 7, 8, 9, 13, 15, 16, 18, 20, 22, 24, 26, 28, 30, 31, 32, 33, 34, 36, 38, 39, 40, 42, 43, 44, 45, 47, 48, 49, 50, 51, 52, 53, 55, 57, 59, 60, 65, 66, 69, 72, 73, 74, 76, 78, 82, 84, 86, 88, 90, 92, 96, 98, 100, 102, 106, 108, 112, 116, 120, 126, 128, 130

Offset: 1

Author

Nicholas Leonard, Jun 19 2023

Keywords

• nonn

Examples

			9 is a term of this sequence as prime(9) mod 9 = 5, which is prime.
		

Links

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

Crossrefs

Cf. A000720, A004648, A363752.

Programs

Mathematica

Table[If[PrimeQ[Mod[Prime[k], k]], k, Nothing], {k, 1, 100}]

PARI

isok(k) = isprime(prime(k) % k); \\ Michel Marcus, Jun 19 2023

Python

from sympy import prime, isprime
a363751=[]
for k in range(1,101):
    if isprime(prime(k)%k):
        a363751.append(k)

Formula

a(n) = A000720(A363752(n)).