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 A071681 Number of ways to represent the n-th prime as arithmetic mean of two other primes. 16
 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; text; internal format)
 OFFSET 1,5 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, Feb 07 2008 The conjecture follows from a slightly strengthened version of Goldbach's conjecture: that every even number > 6 is the sum of two distinct primes. - T. D. Noe, Jan 10 2011 [Corrected by Barry Cherkas and Robert Israel, May 21 2015] a(n) = A116619(n) + 1. - Reinhard Zumkeller, Mar 27 2015 LINKS R. Zumkeller, Table of n, a(n) for n = 1..10000 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}. 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, Mar 22 2007 *) PROG (PARI) A071681(n)={s=2*prime(n); a=0; for(i=1, n-1, a=a+isprime(s-prime(i))); a} (Haskell) a071681 n = sum \$ map a010051' \$    takeWhile (> 0) \$ map (2 * a000040 n -) \$ drop n a000040_list -- Reinhard Zumkeller, Mar 27 2015 CROSSREFS Cf. A071680, A000040, A129363, A178609, A001358, A100484, A001747, A010051, A116619, A253138. Sequence in context: A241568 A047972 A004595 * A135621 A224764 A077268 Adjacent sequences:  A071678 A071679 A071680 * A071682 A071683 A071684 KEYWORD nonn,look AUTHOR Reinhard Zumkeller, May 31 2002 STATUS approved

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Last modified February 7 19:47 EST 2018. Contains 298790 sequences.