A082890 Primes p such that (r-p)/log(p) > 5, where r is the next prime after p.

19609, 25471, 31397, 34061, 35617, 40289, 40639, 43331, 44293, 58831, 79699, 85933, 89689, 102701, 107377, 110359, 124367, 134513, 142993, 149629, 155921, 156157, 162143, 173359, 175141, 186481, 188029, 190409, 203461, 212701, 218287

Offset

1,1

Links

Amiram Eldar, Table of n, a(n) for n = 1..10000

Formula

prime(j) such that (prime(j+1)-prime(j))/log(prime(j)) > 5.

Example

If p = 492113 then r = 492227 and (r-p)/log(p) = 114/log(492113) = 8.69799..., so 492113 is in the sequence.

Mathematica

Do[s=(Prime[n+1]-Prime[n])/Log[Prime[n]]//N; If[s>5, Print[Prime[n]]], {n, 1, 50000}]
seq[len_] := Module[{p = 2, s = {}, c = 0}, While[c < len, q = NextPrime[p]; If[q - p > 5*Log[p], AppendTo[s, p]; c++]; p = q]; s]; seq[31] (* Amiram Eldar, Nov 04 2024 *)

Crossrefs

Cf. A082862, A082884, A082885, A082886, A082888, A082889, A082891.

Sequence in context: A174760 A115472 A022234 * A109569 A204665 A031681

Adjacent sequences: A082887 A082888 A082889 * A082891 A082892 A082893

Keyword

nonn

Author

Labos Elemer, Apr 17 2003

Status

approved