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A270249
Greater of a pair of twin primes (r,s=r+2) where s is of the form p^2 + pq + q^2 and p and q are also twin primes.
1
109, 433, 2056753, 3121201, 3577393, 26462701, 37340353, 43823053, 128786113, 202705201, 304093873, 888345793, 1005988033, 1399680001, 1537437133, 2282300173, 2310187501, 2444964913, 2929312513, 3564542701, 5831255233, 7950571201, 8512439473, 9346947373, 9648752833, 12627464653, 15624660673
OFFSET
1,1
COMMENTS
Subsequence of A243761.
How is the distribution of terms of this sequence? With this form p^2 + pq + q^2, do twin primes generate bigger twin primes infinitely many times?
EXAMPLE
109 is a term because 109 and 107 are twin primes and 109 = 5^2 + 5*7 + 7^2, 5 and 7 are also twin primes.
433 is a term because 433 and 431 are twin primes and 433 = 11^2 + 11*13 + 13^2, 11 and 13 are also twin primes.
PROG
(PARI) t(n, p=3) = {while( p+2 < (p=nextprime( p+1 )) || n-->0, ); p-2}
for(n=1, 1e3, if(ispseudoprime(P=(3*t(n)^2 + 6*t(n) + 4)) && ispseudoprime(P-2), print1(P, ", ")));
(Python)
from itertools import islice
from sympy import isprime, nextprime
def A270249_gen(): # generator of terms
p, q = 2, 3
while True:
if q-p == 2 and isprime(s:=3*p*q+4) and isprime(s-2):
yield s
p, q = q, nextprime(q)
A270249_list = list(islice(A270249_gen(), 20)) # Chai Wah Wu, Feb 27 2023
CROSSREFS
Sequence in context: A166560 A139644 A360490 * A174339 A142640 A126856
KEYWORD
nonn
AUTHOR
Altug Alkan, Mar 14 2016
STATUS
approved