

A178609


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


9



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
(list;
graph;
refs;
listen;
history;
text;
internal format)



OFFSET

1,5


COMMENTS

The plot is very interesting.
a(A178953(n)) = 0.


LINKS

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


EXAMPLE

a(3)=1 because 5=prime(3)=(prime(31)+prime(3+1))/2=(3+7)/2.


MATHEMATICA

Table[k=n1; While[Prime[nk]+Prime[n+k] != 2*Prime[n], k]; k, {n, 100}]


PROG

(Sage) A178609 = lambda n: next(k for k in range(n)[::1] if nth_prime(nk)+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

JuriStepan Gerasimov, Dec 24 2010


EXTENSIONS

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


STATUS

approved



