A082890 - OEIS

%I #11 Nov 04 2024 01:35:22

%S 19609,25471,31397,34061,35617,40289,40639,43331,44293,58831,79699,

%T 85933,89689,102701,107377,110359,124367,134513,142993,149629,155921,

%U 156157,162143,173359,175141,186481,188029,190409,203461,212701,218287

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

%H Amiram Eldar, <a href="/A082890/b082890.txt">Table of n, a(n) for n = 1..10000</a>

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

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

%t Do[s=(Prime[n+1]-Prime[n])/Log[Prime[n]]//N; If[s>5, Print[Prime[n]]], {n, 1, 50000}]

%t 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 *)

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

%K nonn

%O 1,1

%A _Labos Elemer_, Apr 17 2003