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.
2, 4, 8, 14, 38, 98, 344, 22268, 79808, 187124, 347978, 2171618, 4219797674, 98059918334, 22518029924768, 54420534706118, 252534792143648
Offset: 1
Examples
a(5) = 38 because 38+2+1, 38+4+1, 38+8+1 and 38+14+1 are all prime.
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.
Programs
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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 -
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
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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 *)
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
Comments