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A114379 Sums of p-th to the q-th prime where p and q are twin primes. 1
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 (list; graph; refs; listen; history; text; internal format)
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 * A106969 A304390 A309533

Adjacent sequences:  A114376 A114377 A114378 * A114380 A114381 A114382

KEYWORD

easy,nonn

AUTHOR

Cino Hilliard, Feb 10 2006

STATUS

approved

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Last modified August 25 05:19 EDT 2019. Contains 326318 sequences. (Running on oeis4.)