A288908 Primes p whose distance from next prime and from previous prime is greater than log(p).

5, 7, 23, 37, 47, 53, 89, 157, 173, 211, 251, 257, 263, 293, 331, 337, 359, 367, 373, 389, 409, 479, 631, 691, 701, 709, 719, 787, 797, 839, 919, 929, 1163, 1171, 1201, 1249, 1259, 1381, 1399, 1409, 1471, 1511, 1523, 1531, 1637, 1709, 1733, 1801, 1811, 1823

Offset: 1

Author

Giuseppe Coppoletta, Jun 19 2017

Keywords

• nonn

Comments

Primes preceded and followed by larger-than-average prime gaps (see link), then included in A082885.

Examples

			n = 5 is a term because 3 + log(5) < 5 < 7 - log(5).
n = 11 is not a term because 13 - 11 < log(11) = 2.39...
		

Links

• Eric Weisstein's MathWorld, Prime Number Theorem

Crossrefs

Cf. A082885, A151799, A151800, A288907, A330426, A330427, A330428.

Programs

Magma

f:=func;  [p:p in PrimesInInterval(3,2000)|f(p)]; // Marius A. Burtea, Dec 19 2019

Mathematica

Select[Prime@ Range[2, 300], Min@ Abs[# - NextPrime[#, {-1,1}]] > Log[#] &] (* Giovanni Resta, Jun 19 2017 *)

Sage

[n for n in prime_range(3,2000) if next_prime(n)-n>log(n) and n-previous_prime(n)>log(n)]

Formula

A151799(a(n)) + log(a(n)) < a(n) < A151800(a(n)) - log(a(n)).