A353045 Primes of the form p*q*(p+q)+1 where (p,q) is a twin prime pair.

421, 3433, 431881, 746353, 2122213, 84287689, 161242273, 574990681, 1372256173, 6589289569, 8315492209, 13246972549, 40692828541, 52396140061, 75866105281, 77916431221, 82987207333, 91919299573, 140685402049, 152665872493, 188144420089, 199536434869, 265301989801, 404110652329, 406594932241

Offset

1,1

Links

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

Example

a(3) = 431881 is a term because (59, 61) is a twin prime pair with 59*61*(59+61)+1 = 431881, and 431881 is prime.

Maple

P:= select(isprime, {seq(i, i=3..10^6, 2)}):
T:= P intersect map(`-`, P, 2):
R:= map(t -> t*(t+2)*(2*t+2)+1, T):
sort(convert(select(isprime, R), list));

Mathematica

Select[#[[1]]#[[2]]Total[#]+1&/@Select[Partition[Prime[Range[1000]], 2, 1], #[[2]]-#[[1]] == 2&], PrimeQ] (* Harvey P. Dale, Aug 17 2024 *)

Prog

(Python)
from itertools import islice
from sympy import isprime, nextprime
def agen(): # generator of terms
    p, q = 3, 5
    while True:
        if q == p+2:
            t = p*q*(p+q)+1
            if isprime(t):
                yield t
        p, q = q, nextprime(q)
print(list(islice(agen(), 25))) # Michael S. Branicky, Apr 19 2022

Crossrefs

Cf. A001359.

Sequence in context: A068701 A340157 A302284 * A302732 A251198 A302533

Adjacent sequences: A353042 A353043 A353044 * A353046 A353047 A353048

Keyword

nonn

Author

J. M. Bergot and Robert Israel, Apr 19 2022

Status

approved