A087104 Greatest jumping champion for prime(n).

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, 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, 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

Offset: 2

Author

Reinhard Zumkeller, Aug 10 2003

Keywords

• nonn

Comments

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

there are occasionally several jumping champions: see A087102; A087103(n) is the smallest jumping champion for prime(n);

a(n)<=6 for small n, see Odlyzko et al. for primes>1.7*10^35.

Links

• T. D. Noe, Table of n, a(n) for n = 2..1001
• A. Odlyzko, M. Rubinstein and M. Wolf, Jumping Champions
• A. Odlyzko, M. Rubinstein and M. Wolf, Jumping Champions, Experimental Math., 8 (no. 2) (1999).
• Eric Weisstein's World of Mathematics, Jumping Champion

Crossrefs

Cf. A001223, A005250.

Programs

Mathematica

d=Table[0, {100}]; p=2; Table[q=NextPrime[p]; d[[q-p]]++; p=q; Position[d, Max[d]][[-1,1]], {1000}]