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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 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

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