A252837 Let c = A098550. Let c(n) be prime. If c(n+1) is even, then a(n) is the maximal number r of consecutive even numbers of the form c(n+1), c(n+3), ..., c(n+(2r-1)); if c(n+1) is odd, then a(n)=0.

0, 9, 6, 3, 0, 0, 6, 9, 5, 0, 8, 4, 0, 6, 6, 6, 2, 10, 5, 2, 4, 13, 9, 10, 5, 3, 5, 2, 4, 13, 4, 6, 2, 11, 2, 4, 8, 4, 5, 5, 3, 10, 4, 3, 2, 8, 13, 5, 3, 4, 8, 2, 6, 4, 10, 5, 3, 6, 4, 4

Offset

1,2

Comments

Conjecture:

Let c(n)>=43 be prime. Then

1) c(n+1) is even;

2) c(n+(2*a(n)-1)) = 2*q, where q>c(n) is prime;

3) If c(n)>=97 is prime, then in 2) q is the next prime after c(n).

Links

Reinhard Zumkeller, Table of n, a(n) for n = 1..10000

David L. Applegate, Hans Havermann, Bob Selcoe, Vladimir Shevelev, N. J. A. Sloane, and Reinhard Zumkeller, The Yellowstone Permutation, arXiv preprint arXiv:1501.01669, 2015 and J. Int. Seq. 18 (2015) 15.6.7.

Prog

(Haskell)
a252837 n = a252837_list !! (n-1)
a252837_list = f a098550_list where
   f us = (h 0 vs) : f vs where
     (_:vs) = dropWhile ((== 0) . a010051') us
     h e (w:_:ws) = if even w then h (e + 1) ws else e
-- Reinhard Zumkeller, Mar 11 2015

Crossrefs

Cf. A098550, A252838.

Cf. A010051.

Sequence in context: A327996 A357762 A093540 * A198573 A068925 A175616

Adjacent sequences: A252834 A252835 A252836 * A252838 A252839 A252840

Keyword

nonn

Author

Vladimir Shevelev, Dec 22 2014

Status

approved