login
This site is supported by donations to The OEIS Foundation.

 

Logo


Hints
(Greetings from The On-Line Encyclopedia of Integer Sequences!)
A114379 Sums of p-th to the q-th prime where p and q are twin primes. 1

%I

%S 23,41,109,187,349,551,841,1079,1667,1779,2357,2599,3219,3487,3631,

%T 4319,4533,5197,5501,6213,7039,8709,9031,9829,11233,12425,13227,13677,

%U 14329,14813,18667,18951,19073,19973,20561,24329,24685,25153,25561,26261

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

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

%H Danny Rorabaugh, <a href="/A114379/b114379.txt">Table of n, a(n) for n = 1..10000</a>

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

%F a(n) = Sum_{k=A077800(2n-1)..A077800(2n)} prime(k). - _Danny Rorabaugh_, Apr 01 2015

%e 3 and 5 are the first twin prime pair: prime(3) = 5, prime(4) = 7, prime(5) = 11

%e and 5+7+11 = 23, the first entry in the table.

%t Plus @@ (Prime /@ Range[#, # + 2]) & /@ Select[Prime@ Range@ 200, PrimeQ[# + 2] &] (* _Michael De Vlieger_, Apr 01 2015 *)

%o (PARI) sumprimes(m, n) = { local(x); return(sum(x=m, n, prime(x))) }

%o g(n)=forprime(x=3,n,if(isprime(x+2),print1(sumprimes(x,x+2)",")))

%K easy,nonn

%O 1,1

%A _Cino Hilliard_, Feb 10 2006

Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Style Sheet | Transforms | Superseeker | Recent
The OEIS Community | Maintained by The OEIS Foundation Inc.

License Agreements, Terms of Use, Privacy Policy. .

Last modified October 22 07:29 EDT 2019. Contains 328315 sequences. (Running on oeis4.)