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A001043
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Numbers that are the sum of 2 successive primes.
(Formerly M3780 N0968)
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78
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5, 8, 12, 18, 24, 30, 36, 42, 52, 60, 68, 78, 84, 90, 100, 112, 120, 128, 138, 144, 152, 162, 172, 186, 198, 204, 210, 216, 222, 240, 258, 268, 276, 288, 300, 308, 320, 330, 340, 352, 360, 372, 384, 390, 396, 410, 434, 450, 456, 462, 472, 480, 492, 508, 520
(list; graph; refs; listen; history; internal format)
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OFFSET
| 1,1
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COMMENTS
| a(n) = A116366(n,n-1) for n>1. - Reinhard Zumkeller (reinhard.zumkeller(AT)gmail.com), Feb 06 2006
Arithmetic derivative (see A003415) of prime(n)*prime(n+1). [Giorgio Balzarotti (greenblue@tiscali.it), May 26 2011]
A008472(a(n)) = A191583(n). [Reinhard Zumkeller, Jun 28 2011]
With the exception of the first term, all terms are even. a(n) is divisible by 4 if the difference between p(n) and p(n + 1) is not divisible by 4; e.g., p(n) = 1 mod 4 and p(n + 1) = 3 mod 4. In general, for a(n) to be divisible by some even number m > 2 requires that p(n + 1) - p(n) not be a multiple of m. [Alonso del Arte, Jan 30 2012]
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REFERENCES
| Archimedeans Problems Drive, Eureka, 26 (1963), 12.
N. J. A. Sloane, A Handbook of Integer Sequences, Academic Press, 1973 (includes this sequence).
N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).
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LINKS
| T. D. Noe, Table of n, a(n) for n=1..1000
A. Frank & P. Jacqueroux, International Contest, 2001. Item 22
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FORMULA
| a(n) = p(n) + p(n + 1), where p(n) is the n-th prime.
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MATHEMATICA
| Table[Prime[n] + Prime[n+1], {n, 55}] (* Ray Chandler, Feb 12 2005 *)
Total/@Partition[Prime[Range[60]], 2, 1] (* From Harvey P. Dale, Aug 23 2011 *)
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PROG
| (SAGE) BB = primes_first_n(56) list = [] for i in range(55): list.append(BB[1+i]+BB[i]) list # Zerinvary Lajos (zerinvarylajos(AT)yahoo.com), May 14 2007
(MAGMA) [(NthPrime(n+1) + NthPrime(n)): n in [1..100]]; // Vincenzo Librandi, Apr 02 2011
(PARI) p=2; forprime(q=3, 1e3, print1(p+q", "); p=q) \\ Charles R Greathouse IV, Jun 10 2011
(Haskell)
a001043 n = a001043_list !! (n-1)
a001043_list = zipWith (+) a000040_list $ tail a000040_list
-- Reinhard Zumkeller, Oct 19 2011
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CROSSREFS
| Cf. A000040.
Sequence in context: A190708 A145285 A069102 * A118775 A025001 A020749
Adjacent sequences: A001040 A001041 A001042 * A001044 A001045 A001046
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KEYWORD
| nonn,nice,easy,changed
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AUTHOR
| N. J. A. Sloane (njas(AT)research.att.com), R. K. Guy
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EXTENSIONS
| More terms from Larry Reeves (larryr(AT)acm.org), Mar 17 2000
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