A284036 Positive integers n such that (n^2 - 3)/2 and (n^2 + 1)/2 are twin primes.

3, 5, 11, 19, 25, 29, 65, 79, 101, 205, 209, 221, 245, 275, 289, 299, 349, 371, 409, 415, 449, 521, 535, 569, 571, 575, 595, 649, 661, 695, 739, 781, 791, 935, 949, 991, 1081, 1091, 1099, 1129, 1181, 1225, 1241, 1285, 1345, 1349, 1459, 1489, 1531, 1541, 1615

Offset

1,1

Comments

All terms are obviously odd.

Links

Robert Israel, Table of n, a(n) for n = 1..10000

Example

25 is a term because (25^2 - 3)/2 = 311 and (25^2 + 1)/2 = 313 are twin primes.

Maple

filter:= n -> isprime((n^2-3)/2) and isprime((n^2+1)/2):
select(filter, [seq(i, i=1..2000, 2)]); # Robert Israel, Apr 24 2017

Mathematica

Select[Range[1, 1285, 2], Times @@ Boole@ Map[PrimeQ, (#^2 + {-3, 1})/2] == 1 &] (* Michael De Vlieger, Mar 28 2017 *)

Prog

(Sage) [n for n in range(3, 1700, 2) if is_prime((n^2 - 3)//2) and is_prime((n^2 + 1)//2)]
(PARI) isok(n) = isprime((n^2 - 3)/2) && isprime((n^2 + 1)/2); \\ Michel Marcus, Apr 04 2017
(Python)
from sympy import isprime
print([n for n in range(3, 1700, 2) if isprime((n**2 - 3)//2) and isprime((n**2 + 1)//2)]) # Indranil Ghosh, Apr 04 2017

Crossrefs

Cf. A002731, A109358, A048161, A110589, A284034.

Sequence in context: A243899 A168161 A217792 * A172438 A023233 A048161

Adjacent sequences: A284033 A284034 A284035 * A284037 A284038 A284039

Keyword

nonn

Author

Giuseppe Coppoletta, Mar 27 2017

Status

approved