A086870 Primes equal to a product of twin primes minus 1 divided by 2.

7, 17, 71, 449, 881, 2591, 9521, 39761, 106721, 179999, 206081, 342791, 388961, 596231, 847601, 1292831, 2268449, 2571911, 2836961, 3612671, 6223391, 6329681, 6415361, 8520191, 8946449, 9409121, 10342151, 12550049, 16485281, 18800711

Offset: 1

Author

Cino Hilliard, Aug 20 2003

Keywords

• easy
• nonn

Comments

From Jason Kimberley, Oct 22 2015 (Start)

Prime elements of A120876.

For each p in this list, A001221(2p) = A001222(2p) = A001221(2p+1) = A001222(2p+1) = 2.

2*a(n) is a subsequence of A103533. They first differ when 313619 is not in this sequence, but 2*313619 = 627238 = A103533(12).

(End)

Examples

			t1 = 71,t2 = 73, (71*73-1)/2 = 5182/2 = 2591 = prime.
		

Links

• Jason Kimberley, Table of n, a(n) for n = 1..10000

Crossrefs

Cf. A103533, A120876.

Programs

Mathematica

Select[(Times[#, # + 2] - 1)/2 &@ Select[Prime@ Range@ 1000, PrimeQ[# + 2] &], PrimeQ] (* Michael De Vlieger, Nov 06 2015 *)

PARI

for(n=1, 1e3, if(prime(n+1)-prime(n)==2 && isprime(k=(prime(n)*prime(n+1)-1)/2), print1(k", "))) \\ Altug Alkan, Nov 06 2015

Formula

Primes of the form (t1*t2-1)/2, where t1, t2 are twin primes.