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

1,5

Comments

The plot is very interesting.

Links

T. D. Noe, Table of n, a(n) for n = 1..10000

Formula

a(A178953(n)) = 0.

Example

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

Mathematica

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

Prog

(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
(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

Crossrefs

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

Sequence in context: A247602 A201902 A239893 * A144948 A108335 A239474

Adjacent sequences: A178606 A178607 A178608 * A178610 A178611 A178612

Keyword

nonn,look

Author

Juri-Stepan Gerasimov, Dec 24 2010

Extensions

Extended and corrected by T. D. Noe, Dec 28 2010

Status

approved