VOOZH about

URL: https://oeis.org/A339527

⇱ A339527 - OEIS

login
A339527
Primes p for which p + k and p^2 + k are prime, where k = (p^2-1)/12.
2
7, 17, 37, 43, 79, 97, 199, 241, 307, 331, 503, 727, 811, 829, 1297, 1303, 1423, 1879, 2017, 2179, 2593, 2617, 2663, 2953, 3121, 3229, 3761, 3779, 4327, 4357, 4391, 4409, 4663, 4861, 4951, 5021, 5147, 5167, 5237, 5669, 5939, 6569, 7129, 7829, 8269, 8731, 9649, 9781, 10159, 10459, 10531, 10663, 11789
OFFSET
1,1
LINKS
EXAMPLE
a(4) = 43 is a term because with k = (43^2-1)/12 = 154, 43, 43+154 = 197 and 43^2+154 = 2003 are all primes.
MAPLE
select(t -> isprime(t) and isprime((13*t^2-1)/12) and isprime(t+(t^2-1)/12), [seq(seq(12*i+j, j=[1, 5, 7, 11]), i=0..10000)]);
MATHEMATICA
Select[Prime[Range[1500]], AllTrue[(#^2-1)/12+{#, #^2}, PrimeQ]&] (* Harvey P. Dale, Sep 07 2025 *)
PROG
(PARI) isok(p) = isprime(p) && iferr(isprime(p+(p^2-1)/12) && isprime(p^2+(p^2-1)/12), E, 0); \\ Michel Marcus, Dec 23 2020
CROSSREFS
Cf. A081115.
Sequence in context: A101121 A212117 A160635 * A090652 A062675 A257668
KEYWORD
nonn
AUTHOR
J. M. Bergot and Robert Israel, Dec 22 2020
STATUS
approved