

A071681


Number of ways to represent the nth 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
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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*17p 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, n1, a=a+isprime(sprime(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



