

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.


0



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
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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?


LINKS

Table of n, a(n) for n=1..27.


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, ); p2}
for(n=1, 1e3, if(ispseudoprime(P=(3*t(n)^2 + 6*t(n) + 4)) && ispseudoprime(P2), print1(P, ", ")));


CROSSREFS

Cf. A001359, A243761.
Sequence in context: A142846 A166560 A139644 * A174339 A142640 A126856
Adjacent sequences: A270246 A270247 A270248 * A270250 A270251 A270252


KEYWORD

nonn


AUTHOR

Altug Alkan, Mar 14 2016


STATUS

approved



