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

1,1

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)

Links

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

Formula

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

Example

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

Mathematica

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

Prog

(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

Crossrefs

Cf. A103533, A120876.

Sequence in context: A034054 A120876 A216073 * A107693 A217717 A122528

Adjacent sequences: A086867 A086868 A086869 * A086871 A086872 A086873

Keyword

easy,nonn

Author

Cino Hilliard, Aug 20 2003

Status

approved