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A086870 Primes equal to a product of twin primes minus 1 divided by 2. 6
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 (list; graph; refs; listen; history; text; internal format)
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

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Last modified June 16 19:05 EDT 2021. Contains 345068 sequences. (Running on oeis4.)