A372113 Numbers k for which (k-1)/2 and 2*k+1 are both primes.

5, 11, 15, 23, 35, 39, 63, 75, 83, 95, 119, 135, 179, 215, 219, 299, 303, 315, 359, 363, 455, 459, 483, 515, 543, 615, 663, 699, 719, 735, 779, 803, 879, 915, 923, 935, 975, 999, 1019, 1043, 1143, 1155, 1175, 1199, 1295, 1323, 1355, 1383, 1439, 1539, 1595, 1659, 1679, 1755, 1763, 1815, 1859, 1883

Offset

1,1

Comments

Intersection of A072055 and A104635.

Links

Michael De Vlieger, Table of n, a(n) for n = 1..10000

Formula

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

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

Example

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

Mathematica

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

Prog

(Python)
from sympy import isprime
def a(n): return n%2 == 1 and isprime((n-1)>>1) and isprime(2*n+1)
print([n for n in range(2, 1900) if a(n)])

Crossrefs

Cf. A072055, A104635.

Cf. A023213, A126330.

Sequence in context: A314077 A314078 A314079 * A137009 A340131 A290199

Adjacent sequences: A372110 A372111 A372112 * A372114 A372115 A372116

Keyword

nonn

Author

Alexandre Herrera, Apr 19 2024

Status

approved