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Search: id:A093483
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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; listen)
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OFFSET
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1,1
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COMMENT
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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. - njas, 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
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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
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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
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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
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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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CROSSREFS
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Cf. A034881, A103828, A117480, A121404, A103828, A0127903 (primes arising here).
Adjacent sequences: A093480 A093481 A093482 this_sequence A093484 A093485 A093486
Sequence in context: A038024 A061297 A130711 this_sequence A028398 A118884 A118890
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KEYWORD
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hard,nonn,nice
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AUTHOR
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Amarnath Murthy (amarnath_murthy(AT)yahoo.com), Apr 14 2004
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EXTENSIONS
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a(7) from Jonathan Vos Post (jvospost2(AT)yahoo.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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