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Search: id:A120627
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| A120627 |
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Least positive k such that both prime(n)+k and prime(n)+2k are prime, or 0 if no such k exists. |
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+0
2
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| 0, 2, 6, 6, 6, 24, 6, 12, 18, 12, 6, 30, 6, 18, 6, 18, 12, 6, 6, 18, 54, 24, 24, 12, 6, 6, 24, 30, 42, 18, 12, 18, 30, 12, 24, 6, 36, 18, 6, 54, 84, 30, 36, 18, 30, 12, 30, 54, 6, 42, 18, 12, 36, 6, 6, 48, 12, 6, 30, 36, 24, 54, 30, 36, 18, 36, 18, 30, 6, 24, 48, 30, 6, 24, 30, 18, 30
(list; graph; listen)
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OFFSET
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1,2
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COMMENT
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Note that 6 divides a(n) for n>2. - T. D. Noe (noe(AT)sspectra.com), Aug 29 2006
Van der Corput's theorem: There are infinitely many positive integers n, k such that n, n+nk, n+2nk are all prime. - Jonathan Vos Post (jvospost3(AT)gmail.com), Apr 17 2007
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REFERENCES
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A. G. van der Corput, Uber Summen von Primzahlen und Primzahlquadraten," Math. Ann., 116 (1939) 1-50.
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LINKS
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T. D. Noe, Table of n, a(n) for n=1..10000
Terence Tao, Simons Lecture I: Structure and randomness in Fourier analysis and number theory, April 2007.
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EXAMPLE
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a(3)=6 because prime(3)=5 and 5+6 and 5+12 are primes.
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MATHEMATICA
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f[n_] := Block[{p = Prime[n], k = 1}, If[n == 1, 0, While[ ! PrimeQ[p + 2k] || ! PrimeQ[p + 4k], k++ ]; 2k] ]; Table[f[n], {n, 80}] (*Chandler*)
Join[{0}, Table[p=Prime[n]; k=2; While[ !PrimeQ[p+k] || !PrimeQ[p+2k], k=k+2]; k, {n, 2, 100}]] - T. D. Noe (noe(AT)sspectra.com), Aug 29 2006
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CROSSREFS
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Cf. A000040.
Sequence in context: A071888 A117217 A161331 this_sequence A089879 A087651 A078579
Adjacent sequences: A120624 A120625 A120626 this_sequence A120628 A120629 A120630
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KEYWORD
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easy,nonn
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AUTHOR
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Giovanni Teofilatto (g.teofilatto(AT)tiscalinet.it), Aug 25 2006
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EXTENSIONS
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Edited and extended by Ray Chandler (rayjchandler(AT)sbcglobal.net) and T. D. Noe (noe(AT)sspectra.com), Aug 28 2006
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