A372113 - OEIS

%I #27 May 19 2024 06:35:26

%S 5,11,15,23,35,39,63,75,83,95,119,135,179,215,219,299,303,315,359,363,

%T 455,459,483,515,543,615,663,699,719,735,779,803,879,915,923,935,975,

%U 999,1019,1043,1143,1155,1175,1199,1295,1323,1355,1383,1439,1539,1595,1659,1679,1755,1763,1815,1859,1883

%N Numbers k for which (k-1)/2 and 2*k+1 are both primes.

%C Intersection of A072055 and A104635.

%H Michael De Vlieger, <a href="/A372113/b372113.txt">Table of n, a(n) for n = 1..10000</a>

%F a(n) = 2*A023213(n) + 1.

%F a(n) = (A126330(n)-1)/2.

%e 5 is a term because (5-1)/2 = 2 is prime and 2*5+1 = 11 is prime.

%t Select[Range[1, 2000, 2], AllTrue[{(# - 1)/2, 2 # + 1}, PrimeQ] &] (* _Michael De Vlieger_, Apr 19 2024 *)

%o (Python)

%o from sympy import isprime

%o def a(n): return n%2 == 1 and isprime((n-1)>>1) and isprime(2*n+1)

%o print([n for n in range(2, 1900) if a(n)])

%Y Cf. A072055, A104635.

%Y Cf. A023213, A126330.

%K nonn

%O 1,1

%A _Alexandre Herrera_, Apr 19 2024