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A093483
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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.
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5
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2, 4, 8, 14, 38, 98, 344, 22268, 79808, 187124, 347978, 2171618, 4219797674, 98059918334
(list; graph; refs; listen; history; internal format)
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OFFSET
| 1,1
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COMMENTS
| a(i) == 2 mod 6 for i>2. - Walter Kehowski (wkehowski(AT)cox.net), Jun 03 2006
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 (njas(AT)research.att.com), Apr 21 2007
No more terms less than 7*10^12. - David Wasserman (dwasserm(AT)earthlink.net), Apr 3 2007
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REFERENCES
| 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. 44 (1923), 1-70.
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LINKS
| Prime Puzzles and Problems, Set of even numbers { ai } such that every ai + aj + 1 is prime ( i & j are different ).
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EXAMPLE
| a(5) = 38 because 38+2+1, 38+4+1, 38+8+1 and 38+14+1 are all prime.
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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 (wkehowski(AT)cox.net), Jun 03 2006
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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
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CROSSREFS
| Cf. A034881, A103828, A117480, A121404, A103828.
Cf. A010051.
Sequence in context: A038024 A061297 A130711 * A028398 A155249 A113553
Adjacent sequences: A093480 A093481 A093482 * A093484 A093485 A093486
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KEYWORD
| hard,nonn,nice
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AUTHOR
| Amarnath Murthy (amarnath_murthy(AT)yahoo.com), Apr 14 2004
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EXTENSIONS
| a(7) from Jonathan Vos Post (jvospost3(AT)gmail.com), Mar 22 2006
More terms from Joshua Zucker (joshua.zucker(AT)stanfordalumni.org), Jul 24 2006
Edited and extended to a(14) by David Wasserman (dwasserm(AT)earthlink.net), Apr 03 2007
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