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A060769 "Overdue" primes: upper ends of prime gaps that are larger than the prime number theorem predicts. 4

%I #8 Jul 03 2018 02:26:40

%S 29,37,53,59,67,79,89,97,127,149,191,211,223,251,293,307,331,347,367,

%T 397,409,419,431,457,479,487,499,521,541,557,587,631,641,673,691,701,

%U 709,719,727,751,769

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

%H Harry J. Smith, <a href="/A060769/b060769.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 79 is in the sequence because 79/log(79) - 73/log(73) = 1.065... > 1.

%o (PARI) { default(realprecision, 100); n=0; s=2/log(2); forprime (p=3, 26203, if ((r=p/log(p)) - s > 1, write("b060769.txt", n++, " ", p); ); s=r; ) } \\ _Harry J. Smith_, Jul 11 2009

%Y Cf. A060770, A060771.

%Y Apart from 2 this is the complementary prime set to A060770.

%K nonn

%O 1,1

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

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Last modified May 14 22:35 EDT 2024. Contains 372533 sequences. (Running on oeis4.)