A252837 - OEIS

%I #30 May 15 2018 16:48:41

%S 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,

%T 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

%N 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.

%C Conjecture:

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

%C 1) c(n+1) is even;

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

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

%H Reinhard Zumkeller, <a href="/A252837/b252837.txt">Table of n, a(n) for n = 1..10000</a>

%H 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 <a href="https://cs.uwaterloo.ca/journals/JIS/VOL18/Sloane/sloane9.html">J. Int. Seq. 18 (2015) 15.6.7</a>.

%o (Haskell)

%o a252837 n = a252837_list !! (n-1)

%o a252837_list = f a098550_list where

%o    f us = (h 0 vs) : f vs where

%o      (_:vs) = dropWhile ((== 0) . a010051') us

%o      h e (w:_:ws) = if even w then h (e + 1) ws else e

%o -- _Reinhard Zumkeller_, Mar 11 2015

%Y Cf. A098550, A252838.

%Y Cf. A010051.

%K nonn

%O 1,2

%A _Vladimir Shevelev_, Dec 22 2014