A231652 Lesser twin prime p such that p^2-p-2 is the average of a larger twin prime pair.

5, 11, 17, 29, 71, 197, 269, 1277, 1289, 1607, 2027, 2111, 2267, 2687, 3467, 4649, 6359, 6761, 6827, 7877, 9461, 10529, 12917, 13337, 13691, 13829, 13931, 17291, 17579, 20441, 20771, 26249, 29021, 29129, 34589, 34649, 38237, 39239, 44027, 47417, 49547, 51347

Offset

1,1

Comments

There are 265364 members of this sequence up to 10^10, so about 1% of twin primes with fewer than 10 digits are in this sequence. - Charles R Greathouse IV, Nov 12 2013

Links

Michael G. Kaarhus, Table of n, a(n) for n = 1..10000

M. G. Kaarhus, newprime.pdf

Example

17 is in this sequence because 17 is a lesser twin prime and 17^2 - 17 - 2 is the average of 269 and 271 which is a pair of twin primes.

Prog

(Maxima) y:0$ p:0$ c:0$ f(p):= p^2-p-2$ for p:5 thru 100000 step 6 do (if(primep(p) and primep(p+2)) then (y:f(p), if(primep(y-1) and primep(y+1)) then (c:c+1, print(c, ", ", p, ", ", y))))
(PARI) is(n)=isprime(n^2-n-3) && isprime(n^2-n-1) && isprime(n+2) && isprime(n) && n>3 \\ Charles R Greathouse IV, Nov 12 2013

Crossrefs

Subsequence of A001359.

Sequence in context: A268518 A268521 A230138 * A321792 A068072 A136292

Adjacent sequences: A231649 A231650 A231651 * A231653 A231654 A231655

Keyword

nonn

Author

Michael G. Kaarhus, Nov 12 2013

Status

approved