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

1,1

Comments

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

Links

Table of n, a(n) for n=1..50.

Eric Weisstein's MathWorld, Prime Number Theorem

Formula

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

Example

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...

Mathematica

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

Prog

(Sage) [n for n in prime_range(3, 2000) if next_prime(n)-n>log(n) and n-previous_prime(n)>log(n)]
(Magma)  f:=func<p|Abs(p-NextPrime(p)) gt Log(p) and Abs(p-PreviousPrime(p)) gt Log(p)>;  [p:p in PrimesInInterval(3, 2000)|f(p)]; // Marius A. Burtea, Dec 19 2019

Crossrefs

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

Sequence in context: A018656 A214520 A156123 * A166251 A167936 A077242

Adjacent sequences: A288905 A288906 A288907 * A288909 A288910 A288911

Keyword

nonn

Author

Giuseppe Coppoletta, Jun 19 2017

Status

approved