OFFSET
1,1
COMMENTS
If the sum is a member of a twin prime pair, it always is the upper member, shown in A158866.
Moreover, except the first term, these numbers are of the form 10k+1. [We prove this by exhausting the possibilities when calculating the upper, summing and inspecting the lower of the sum. Here are the possible outcomes.
p1(k), p2(k) p2(m) = p1(k)+p2(k)+1
------------ ---------------------------------
10k+1 10k+3 20k+4+1 not prime
10k+3 10k+5 p2(k) not prime
10k+5 10k+7 p1(k) not prime
10k+7 10k+9 20k+16+1 upper => p1(m) not prime
10k+9 10k+11 20k+20+1 = 10(2k+2)+1
So the only form that was not eliminated, is 10k+1. 13 defies this scheme because 10k+5 is prime for k=0, Q.E.D.]
LINKS
Harvey P. Dale, Table of n, a(n) for n = 1..1000
FORMULA
EXAMPLE
The 30th lower twin prime is 659. 659+661+1 = 1321, prime and 1319 is too.
Then 1319 is the lower member of the twin prime pair (1319,1321). So 1321 is in the sequence.
MATHEMATICA
With[{tws=Total/@Select[Partition[Prime[Range[25000]], 2, 1], #[[2]]-#[[1]] == 2&]+1}, Select[tws, And@@PrimeQ[#+{0, -2}]&]] (* Harvey P. Dale, Apr 30 2014 *)
PROG
(PARI) gp > g(n)=for(x=1, n, y=2*twinl(x)+3; if(isprime(y)&&isprime(y-2), print1(y", ")))
CROSSREFS
KEYWORD
nonn
AUTHOR
Cino Hilliard, Mar 28 2009
EXTENSIONS
Edited by R. J. Mathar, Apr 06 2009
STATUS
approved