|
%I #10 Mar 30 2012 18:50:37
%S 1,2,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,2,1,2,1,2,2,1,1,2,2,
%T 1,1,1,2,2,3,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,
%U 1,1,1,1,1,2,2,1,1,1,1,1,2,2,1,2,2,1,1,1,2,3,3,3,1,1,1,1,1,1,1,2,2,1
%N Number of numbers occurring most frequently as difference between consecutive primes <= prime(n).
%C For small n: a(n)<=3; A087103(n) and A087104(n) give the smallest and greatest jumping champion(s) for prime(n).
%H T. D. Noe, <a href="/A087102/b087102.txt">Table of n, a(n) for n = 2..1001</a>
%H A. Odlyzko, M. Rubinstein and M. Wolf, <a href="http://www.dtc.umn.edu/~odlyzko/doc/jumping.champions.pdf">Jumping Champions</a>
%H A. Odlyzko, M. Rubinstein and M. Wolf, <a href="http://www.emis.de/journals/EM/expmath/volumes/8/8.html">Jumping Champions</a>, Experimental Math., 8 (no. 2) (1999).
%H Eric Weisstein's World of Mathematics, <a href="http://mathworld.wolfram.com/JumpingChampion.html">Jumping Champion</a>
%t d=Table[0, {100}]; p=2; Table[q=NextPrime[p]; d[[q-p]]++; p=q; Length[Position[d, Max[d]]], {1000}]
%Y Cf. A001223, A005250.
%K nonn
%O 2,2
%A _Reinhard Zumkeller_, Aug 10 2003
|
