A087102 Number of numbers occurring most frequently as difference between consecutive primes <= prime(n).

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, 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, 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

Offset: 2

Author

Reinhard Zumkeller, Aug 10 2003

Keywords

• nonn

Comments

For small n: a(n)<=3; A087103(n) and A087104(n) give the smallest and greatest jumping champion(s) for prime(n).

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; Length[Position[d, Max[d]]], {1000}]