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A288907 Primes p whose distance from next prime and from previous prime is less than log(p). 1
71, 101, 103, 107, 109, 193, 197, 227, 229, 281, 311, 313, 349, 433, 439, 443, 461, 463, 503, 563, 569, 571, 593, 599, 601, 607, 613, 617, 643, 647, 653, 659, 677, 733, 739, 757, 823, 827, 857, 859, 881, 883, 941, 947, 971, 977, 1013, 1019, 1033, 1063, 1091, 1093 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,1

COMMENTS

Primes preceded and followed by lesser-than-average prime gaps (by Prime Number Theorem, see link).

LINKS

Table of n, a(n) for n=1..52.

Eric Weisstein's MathWorld, Prime Number Theorem

FORMULA

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

EXAMPLE

n = 23 is not a term because 23 - 19 > log(23) = 3.13...

n = 71 is a term because log(71) = 4.71.. and 73 - log(71) < 71 < 67 + log(71).

MATHEMATICA

Select[Range[2, 220] // Prime, Max[ Abs[# - NextPrime[#, {-1, 1}]]] < Log[#] &] (* Giovanni Resta, Jun 19 2017 *)

PROG

(Sage) [n for n in prime_range(3, 1300) if next_prime(n)-n<log(n) and n-previous_prime(n)<log(n)] #

(PARI) is(n) = ispseudoprime(n) && n-precprime(n-1) < log(n) && nextprime(n+1)-n < log(n) \\ Felix Fröhlich, Jun 19 2017

CROSSREFS

Cf. A151799, A151800, A288908.

Sequence in context: A023282 A155953 A247200 * A234962 A166252 A339466

Adjacent sequences:  A288904 A288905 A288906 * A288908 A288909 A288910

KEYWORD

nonn

AUTHOR

Giuseppe Coppoletta, Jun 19 2017

STATUS

approved

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Last modified July 28 09:54 EDT 2021. Contains 346326 sequences. (Running on oeis4.)