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A060770 "Early" primes: upper ends of prime gaps that are smaller than the prime number theorem predicts. 2

%I

%S 3,5,7,11,13,17,19,23,31,41,43,47,61,71,73,83,101,103,107,109,113,131,

%T 137,139,151,157,163,167,173,179,181,193,197,199,227,229,233,239,241,

%U 257,263,269,271,277,281,283,311

%N "Early" primes: upper ends of prime gaps that are smaller than the prime number theorem predicts.

%H Harry J. Smith, <a href="/A060770/b060770.txt">Table of n, a(n) for n = 1..1000</a>

%F A prime p belongs to the sequence iff p/log(p) - q/log(q) < 1 where q is the preceding prime.

%e 11 is in the sequence because 11/log(11) - 7/log(7) = 0.990... < 1.

%o (PARI) { default(realprecision, 100); n=0; s=2/log(2); forprime (p=3, 12583, if ((r=p/log(p)) - s < 1, write("b060770.txt", n++, " ", p); ); s=r; ) } \\ _Harry J. Smith_, Jul 11 2009

%Y Apart from 2 this is the complementary prime set to A060769.

%K nonn

%O 1,1

%A Ulrich Schimke (ulrschimke(AT)aol.com)

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Last modified March 22 04:32 EDT 2019. Contains 321406 sequences. (Running on oeis4.)