cp's OEIS Frontend

A178609 Largest k < n such that prime(n-k) + prime(n+k) = 2*prime(n).

%I A178609 #26 Feb 27 2020 04:21:25
%S A178609 0,0,1,0,3,2,2,0,0,5,3,6,4,0,0,7,7,4,8,10,0,0,7,4,11,6,2,2,0,0,13,9,
%T A178609 10,12,0,2,16,0,6,12,13,4,19,17,15,0,18,0,0,0,11,0,0,3,1,1,0,0,6,0,0,
%U A178609 0,27,13,0,0,17,5,29,23,26,20,26,11,7,21,20,15,19,34,21,2,21,11,10,10,10,27,3,0,0,5,32,2,0,0,0,26,0,33
%N A178609 Largest k < n such that prime(n-k) + prime(n+k) = 2*prime(n).
%C A178609 The plot is very interesting.
%H A178609 T. D. Noe, <a href="/A178609/b178609.txt">Table of n, a(n) for n = 1..10000</a>
%F A178609 a(A178953(n)) = 0.
%e A178609 a(3)=1 because 5=prime(3)=(prime(3-1)+prime(3+1))/2=(3+7)/2.
%t A178609 Table[k=n-1; While[Prime[n-k]+Prime[n+k] != 2*Prime[n], k--]; k, {n,100}]
%o A178609 (Sage)
%o A178609 def A178609(n):
%o A178609     return next(k for k in range(n)[::-1] if nth_prime(n-k)+nth_prime(n+k) == 2*nth_prime(n))
%o A178609 # _D. S. McNeil_, Dec 29 2010
%o A178609 (Haskell)
%o A178609 a178609 n = head [k | k <- [n - 1, n - 2 .. 0], let p2 = 2 * a000040 n,
%o A178609                       a000040 (n - k) + a000040 (n + k) == p2]
%o A178609 -- _Reinhard Zumkeller_, Jan 30 2014
%Y A178609 Cf. A006562 (balanced primes), A178670 (number of k), A178698 (composite case), A179835 (smallest k).
%K A178609 nonn,look
%O A178609 1,5
%A A178609 _Juri-Stepan Gerasimov_, Dec 24 2010
%E A178609 Extended and corrected by _T. D. Noe_, Dec 28 2010