A288908 - OEIS

%I #27 Sep 08 2022 08:46:19

%S 5,7,23,37,47,53,89,157,173,211,251,257,263,293,331,337,359,367,373,

%T 389,409,479,631,691,701,709,719,787,797,839,919,929,1163,1171,1201,

%U 1249,1259,1381,1399,1409,1471,1511,1523,1531,1637,1709,1733,1801,1811,1823

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

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

%H Eric Weisstein's MathWorld, <a href="http://mathworld.wolfram.com/PrimeNumberTheorem.html">Prime Number Theorem</a>

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

%e n = 5 is a term because 3 + log(5) < 5 < 7 - log(5).

%e n = 11 is not a term because 13 - 11 < log(11) = 2.39...

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

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

%o (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

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

%K nonn

%O 1,1

%A _Giuseppe Coppoletta_, Jun 19 2017