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A087104 Greatest jumping champion for prime(n).

%I A087104 #11 Feb 16 2025 08:32:50
%S A087104 1,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,4,2,4,2,4,4,4,4,4,4,
%T A087104 2,2,2,4,4,6,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,
%U A087104 2,2,2,2,2,6,6,6,6,6,6,6,6,6,2,6,6,6,6,6,6,6,6,6,4,4,4,4,4,4,4,6,6,6
%N A087104 Greatest jumping champion for prime(n).
%C A087104 A number is called a jumping champion for n, if it is the most frequently occurring difference between consecutive primes <= n;
%C A087104 there are occasionally several jumping champions: see A087102; A087103(n) is the smallest jumping champion for prime(n);
%C A087104 a(n)<=6 for small n, see Odlyzko et al. for primes>1.7*10^35.
%H A087104 T. D. Noe, <a href="/A087104/b087104.txt">Table of n, a(n) for n = 2..1001</a>
%H A087104 A. Odlyzko, M. Rubinstein and M. Wolf, <a href="http://www.dtc.umn.edu/~odlyzko/doc/jumping.champions.pdf">Jumping Champions</a>
%H A087104 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 A087104 Eric Weisstein's World of Mathematics, <a href="https://mathworld.wolfram.com/JumpingChampion.html">Jumping Champion</a>
%t A087104 d=Table[0, {100}]; p=2; Table[q=NextPrime[p]; d[[q-p]]++; p=q; Position[d, Max[d]][[-1,1]], {1000}]
%Y A087104 Cf. A001223, A005250.
%K A087104 nonn
%O A087104 2,2
%A A087104 _Reinhard Zumkeller_, Aug 10 2003