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

2,2

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

Mathematica

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

Crossrefs

Cf. A001223, A005250.

Sequence in context: A086858 A111892 A108248 * A343743 A069926 A077429

Adjacent sequences: A087101 A087102 A087103 * A087105 A087106 A087107

Keyword

nonn

Author

Reinhard Zumkeller, Aug 10 2003

Status

approved