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Primes p such that (r-p)/log(p) > 3, where r is the next prime after p.
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%I #13 Nov 04 2024 01:35:15

%S 1129,1327,1669,2179,2477,2971,3137,3271,4297,4831,5119,5351,5531,

%T 5591,5749,5953,6491,6917,7253,7759,7963,8389,8467,8893,8971,9551,

%U 9973,10009,10399,10531,10799,10909,11743,12163,12853,13063,13187,13933

%N Primes p such that (r-p)/log(p) > 3, where r is the next prime after p.

%H Amiram Eldar, <a href="/A082888/b082888.txt">Table of n, a(n) for n = 1..10000</a> (terms 1..1000 from Harvey P. Dale)

%F prime(j) such that (prime(j+1)-prime(j))/log(prime(j)) > 3.

%e If p = 1327 then r = 1361 and (r-p)/log(p) = 34/log(1327) = 4.72834..., so 1327 is in the sequence.

%t Do[s=(Prime[n+1]-Prime[n])/Log[Prime[n]]//N; If[s>3, Print[Prime[n]]], {n, 1, 2000}]

%t Transpose[Select[Partition[Prime[Range[2000]],2,1],(Last[#]-First[#])/ Log[ First[ #]]>3&]][[1]] (* _Harvey P. Dale_, Apr 20 2013 *)

%Y Cf. A082862, A082884, A082885, A082886, A082889, A082890, A082891.

%K nonn

%O 1,1

%A _Labos Elemer_, Apr 17 2003