|
|
A093483
|
|
a(1) = 2; for n>1, a(n) = smallest integer > a(n-1) such that a(n) + a(i) + 1 is prime for all 1 <= i <= n-1.
|
|
9
|
|
|
2, 4, 8, 14, 38, 98, 344, 22268, 79808, 187124, 347978, 2171618, 4219797674, 98059918334, 22518029924768, 54420534706118, 252534792143648
(list;
graph;
refs;
listen;
history;
text;
internal format)
|
|
|
OFFSET
|
1,1
|
|
COMMENTS
|
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
|
|
LINKS
|
|
|
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
|
|
CROSSREFS
|
|
|
KEYWORD
|
hard,nonn,nice
|
|
AUTHOR
|
|
|
EXTENSIONS
|
|
|
STATUS
|
approved
|
|
|
|