A081531 - OEIS

A081531

Primes p such that (r-p)/log(p) > 2, where r is the next prime after p.

7, 113, 139, 199, 211, 293, 317, 523, 773, 839, 863, 887, 953, 1069, 1129, 1259, 1327, 1381, 1637, 1669, 1759, 1831, 1913, 1933, 1951, 2113, 2161, 2179, 2221, 2251, 2311, 2477, 2503, 2557, 2593, 2803, 2861, 2971, 3089, 3137, 3229, 3271, 3413, 3469, 3739

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OFFSET

1,1

LINKS

Harvey P. Dale, Table of n, a(n) for n = 1..1000

FORMULA

prime(j) such that (prime(j+1)-prime(j))/log(prime(j)) > 2.

EXAMPLE

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

MATHEMATICA

Do[s=(Prime[n+1]-Prime[n])/Log[Prime[n]]//N; If[s>2, Print[Prime[n]]], {n, 1, 2000}]

Transpose[Select[Partition[Prime[Range[600]], 2, 1], (Last[#]-First[#])/ Log[ First[#]]>2&]][[1]] (* Harvey P. Dale, Jun 22 2014 *)