A144309 a(n) is the index of the smallest prime such that the gap to the next prime is not less than 2*n.

2, 4, 9, 24, 30, 30, 30, 99, 99, 154, 189, 217, 217, 217, 217, 217, 217, 1183, 1831, 1831, 1831, 1831, 2225, 2225, 2225, 2225, 3385, 3385, 3385, 3385, 3385, 3385, 3385, 3385, 3385, 3385, 14357, 14357, 14357, 14357, 14357, 14357, 14357, 30802, 30802, 30802

Offset: 1

Author

Artur Jasinski, Sep 17 2008

Keywords

• nonn

Links

• Amiram Eldar, Table of n, a(n) for n = 1..775

Crossrefs

For indices of smallest prime such that gap to next prime is exactly equal to 2*n see A000230. For records in this sequence see A005669.

Cf. A000720, A100964.

Programs

Mathematica

a = {}; Do[n = 1; While[(Prime[n + 1] - Prime[n]) < 2 k, n++ ]; AppendTo[a, n], {k, 1, 75}]; a

PARI

lista(pmax) = {my(k = 1, prv = 2, m = 2, kprv = 2); forprime(p = 3, pmax, k++; if(p - prv >= m, for(i = 1, (p - prv - m)/2 + 1, print1(k-1, ", ")); m = p - prv + 2; kprv = k); prv = p);} \\ Amiram Eldar, Sep 06 2024

Formula

a(n) = primepi(A100964(n)) = A000720(A100964(n)). - Michel Marcus, Nov 02 2013