A178609 - OEIS

%I #26 Feb 27 2020 04:21:25

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

%C The plot is very interesting.

%H T. D. Noe, <a href="/A178609/b178609.txt">Table of n, a(n) for n = 1..10000</a>

%F a(A178953(n)) = 0.

%e a(3)=1 because 5=prime(3)=(prime(3-1)+prime(3+1))/2=(3+7)/2.

%t Table[k=n-1; While[Prime[n-k]+Prime[n+k] != 2*Prime[n], k--]; k, {n,100}]

%o (Sage)

%o def A178609(n):

%o     return next(k for k in range(n)[::-1] if nth_prime(n-k)+nth_prime(n+k) == 2*nth_prime(n))

%o # _D. S. McNeil_, Dec 29 2010

%o (Haskell)

%o a178609 n = head [k | k <- [n - 1, n - 2 .. 0], let p2 = 2 * a000040 n,

%o                       a000040 (n - k) + a000040 (n + k) == p2]

%o -- _Reinhard Zumkeller_, Jan 30 2014

%Y Cf. A006562 (balanced primes), A178670 (number of k), A178698 (composite case), A179835 (smallest k).

%K nonn,look

%O 1,5

%A _Juri-Stepan Gerasimov_, Dec 24 2010

%E Extended and corrected by _T. D. Noe_, Dec 28 2010