OFFSET
1,1
COMMENTS
a(i) == 2 mod 6 for i > 2. - Walter Kehowski, Jun 03 2006
a(i) == either 8 or 14 (mod 30) for i > 2. - Robert G. Wilson v, Oct 16 2012
The Hardy-Littlewood k-tuple conjecture would imply that this sequence is infinite. Note that, for n > 2, a(n)+3 and a(n)+5 are both primes, so a proof that this sequence is infinite would also show that there are infinitely many twin primes. - N. J. A. Sloane, Apr 21 2007
No more terms less than 7*10^12. - David Wasserman, Apr 03 2007
LINKS
G. H. Hardy and J. E. Littlewood, Some problems of 'Partitio numerorum'; III: On the expression of a number as a sum of primes, Acta Math., Vol. 44, No. 1 (1923), pp. 1-70.
Carlos Rivera, Puzzle 37. Set of even numbers { ai } such that every ai + aj + 1 is prime ( i & j are different ), The Prime Puzzles and Problems Connection.
EXAMPLE
a(5) = 38 because 38+2+1, 38+4+1, 38+8+1 and 38+14+1 are all prime.
MAPLE
EP:=[2, 4]: P:=[]: for w to 1 do for n from 1 to 800*10^6 do s:=6*n+2; Q:=map(z-> z+s+1); if andmap(isprime, Q) then EP:=[op(EP), s]; P:=[op(P), op(Q)] fi; od od; EP; P: # Walter Kehowski, Jun 03 2006
MATHEMATICA
f[1] = 2; f[2] = 4; f[3] = 8; f[n_] := f[n] = Block[{lst = Array[f, n - 1], k = f[n - 1] + 7}, While[ Union[ PrimeQ[k + lst]] != {True}, k += 6]; k-1]; Array[f, 13] (* Robert G. Wilson v, Oct 16 2012 *)
PROG
(Haskell)
a093483 n = a093483_list !! (n-1)
a093483_list = f ([2..7] ++ [8, 14..]) [] where
f (x:xs) ys = if all (== 1) $ map (a010051 . (+ x)) ys
then x : f xs ((x+1):ys) else f xs ys
-- Reinhard Zumkeller, Dec 11 2011
CROSSREFS
KEYWORD
hard,nonn,nice
AUTHOR
Amarnath Murthy, Apr 14 2004
EXTENSIONS
a(7) from Jonathan Vos Post, Mar 22 2006
More terms from Joshua Zucker, Jul 24 2006
Edited and extended to a(14) by David Wasserman, Apr 03 2007
a(15)-a(17) from Don Reble, added by N. J. A. Sloane, Sep 18 2012
STATUS
approved