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

1,1

Comments

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

Links

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

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

Example

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.

Mathematica

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

Prog

(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)", ")))

Crossrefs

Sequence in context: A153037 A106970 A155702 * A345099 A106969 A343816

Adjacent sequences: A114376 A114377 A114378 * A114380 A114381 A114382

Keyword

easy,nonn

Author

Cino Hilliard, Feb 10 2006

Status

approved