A114379 Sums of p-th to the q-th prime where p and q are twin primes.

23, 41, 109, 187, 349, 551, 841, 1079, 1667, 1779, 2357, 2599, 3219, 3487, 3631, 4319, 4533, 5197, 5501, 6213, 7039, 8709, 9031, 9829, 11233, 12425, 13227, 13677, 14329, 14813, 18667, 18951, 19073, 19973, 20561, 24329, 24685, 25153, 25561, 26261

Offset: 1

Author

Cino Hilliard, Feb 10 2006

Keywords

• easy
• nonn

Comments

Conjecture: The number of terms in this sequence is infinite.

Examples

			3 and 5 are the first twin prime pair: prime(3) = 5, prime(4) = 7, prime(5) = 11
and 5+7+11 = 23, the first entry in the table.
		

Links

• Danny Rorabaugh, Table of n, a(n) for n = 1..10000

Programs

Mathematica

Plus @@ (Prime /@ Range[#, # + 2]) & /@ Select[Prime@ Range@ 200, PrimeQ[# + 2] &] (* Michael De Vlieger, Apr 01 2015 *)

PARI

sumprimes(m, n) = { local(x); return(sum(x=m, n, prime(x))) }
g(n)=forprime(x=3,n,if(isprime(x+2),print1(sumprimes(x,x+2)",")))

Formula

prime(k) = A000040(k) is the k-th prime number.

a(n) = Sum_{k=A077800(2n-1)..A077800(2n)} prime(k). - Danny Rorabaugh, Apr 01 2015