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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)); 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

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Last modified September 10 20:10 EDT 2024. Contains 375794 sequences. (Running on oeis4.)