A087103 - OEIS

%I #14 Apr 01 2022 09:13:28

%S 1,1,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,4,4,2,2,

%T 2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,

%U 2,2,2,2,2,2,2,6,6,6,6,6,2,2,2,2,2,6,6,6,2,2,2,2,4,4,4,4,4,4,4,4,4,6

%N Smallest jumping champion for prime(n).

%C A number is called a jumping champion for n, if it is the most frequently occurring difference between consecutive primes <= n;

%C there are occasionally several jumping champions: see A087102; A087104(n) is the greatest jumping champion for prime(n).

%H T. D. Noe, <a href="/A087103/b087103.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; Position[d, Max[d]][[1,1]], {1000}]

%Y Cf. A001223, A005250.

%K nonn

%O 2,3

%A _Reinhard Zumkeller_, Aug 10 2003