A178609 Largest k < n such that prime(n-k) + prime(n+k) = 2*prime(n).
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, 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, 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
Offset: 1
Examples
a(3)=1 because 5=prime(3)=(prime(3-1)+prime(3+1))/2=(3+7)/2.
Links
- T. D. Noe, Table of n, a(n) for n = 1..10000
Crossrefs
Programs
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Haskell
a178609 n = head [k | k <- [n - 1, n - 2 .. 0], let p2 = 2 * a000040 n, a000040 (n - k) + a000040 (n + k) == p2] -- Reinhard Zumkeller, Jan 30 2014 -
Mathematica
Table[k=n-1; While[Prime[n-k]+Prime[n+k] != 2*Prime[n], k--]; k, {n,100}] -
Sage
def A178609(n): return next(k for k in range(n)[::-1] if nth_prime(n-k)+nth_prime(n+k) == 2*nth_prime(n)) # D. S. McNeil, Dec 29 2010
Formula
a(A178953(n)) = 0.
Extensions
Extended and corrected by T. D. Noe, Dec 28 2010
Comments