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

Author

Michael G. Kaarhus, Nov 12 2013

Keywords

• nonn

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

Examples

			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.
		

Links

• Michael G. Kaarhus, Table of n, a(n) for n = 1..10000
• M. G. Kaarhus, newprime.pdf

Crossrefs

Subsequence of A001359.

Programs

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