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A071681
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Number of ways to represent the n-th prime as arithmetic mean of two other primes.
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12
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0, 0, 1, 1, 2, 2, 3, 1, 3, 3, 2, 4, 4, 4, 4, 5, 5, 3, 5, 7, 5, 4, 5, 6, 6, 8, 6, 7, 6, 6, 8, 8, 10, 6, 10, 8, 8, 6, 10, 8, 9, 7, 9, 11, 10, 6, 10, 11, 11, 8, 12, 10, 10, 14, 13, 14, 13, 9, 10, 13, 12, 12, 14, 16, 11, 13, 13, 14, 18, 13, 18, 14, 14, 17, 14, 16, 14, 16, 15, 16, 16, 17, 16, 16
(list; graph; refs; listen; history; internal format)
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OFFSET
| 1,5
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COMMENTS
| Conjecture: a(n)>0 for n>2.
a(A137700(n))=n and a(m)<>n for m < A137700(n), A000040(A137700(n))=A126204(n). - Reinhard Zumkeller (reinhard.zumkeller(AT)gmail.com), Feb 07 2008
The conjecture follows from the Goldbach conjecture.
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LINKS
| R. Zumkeller, Table of n, a(n) for n = 1..10000
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EXAMPLE
| a(7)=3 as prime(7) = 17 = (3+31)/2 = (5+29)/2 = (11+23)/2 and 2*17-p is not prime for the other primes p<17: {2,7,13}.
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MATHEMATICA
| f[n_] := Block[{c = 0, k = PrimePi@n - 1}, While[k > 0, If[ PrimeQ[2n - Prime@k], c++ ]; k-- ]; c]; Table[ f@ Prime@n, {n, 84}] (* Robert G. Wilson v (rgwv(AT)rgwv.com), Mar 22 2007 *)
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PROG
| (PARI) A071681(n)={s=2*prime(n); a=0; for(i=1, n-1, a=a+isprime(s-prime(i))); a}
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CROSSREFS
| Cf. A071680
Cf. A000040, A129363, A178609, A001358, A100484, A001747
Sequence in context: A047972 A088741 A004595 * A135621 A077268 A162911
Adjacent sequences: A071678 A071679 A071680 * A071682 A071683 A071684
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KEYWORD
| nonn
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AUTHOR
| Reinhard Zumkeller (reinhard.zumkeller(AT)gmail.com), May 31 2002
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