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A353045 Primes of the form p*q*(p+q)+1 where (p,q) is a twin prime pair. 1
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 (list; graph; refs; listen; history; text; internal format)
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));

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

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Last modified June 24 21:51 EDT 2022. Contains 354830 sequences. (Running on oeis4.)