login
Numbers k such that prime(k) mod k is prime.
2

%I #27 Sep 06 2024 11:48:01

%S 3,4,7,8,9,13,15,16,18,20,22,24,26,28,30,31,32,33,34,36,38,39,40,42,

%T 43,44,45,47,48,49,50,51,52,53,55,57,59,60,65,66,69,72,73,74,76,78,82,

%U 84,86,88,90,92,96,98,100,102,106,108,112,116,120,126,128,130

%N Numbers k such that prime(k) mod k is prime.

%H Amiram Eldar, <a href="/A363751/b363751.txt">Table of n, a(n) for n = 1..10000</a>

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

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

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

%o (Python)

%o from sympy import prime, isprime

%o a363751=[]

%o for k in range(1,101):

%o if isprime(prime(k)%k):

%o a363751.append(k)

%o (PARI) isok(k) = isprime(prime(k) % k); \\ _Michel Marcus_, Jun 19 2023

%Y Cf. A000720, A004648, A363752.

%K nonn

%O 1,1

%A _Nicholas Leonard_, Jun 19 2023