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

29, 37, 53, 59, 67, 79, 89, 97, 127, 149, 191, 211, 223, 251, 293, 307, 331, 347, 367, 397, 409, 419, 431, 457, 479, 487, 499, 521, 541, 557, 587, 631, 641, 673, 691, 701, 709, 719, 727, 751, 769

Offset

1,1

Links

Harry J. Smith, Table of n, a(n) for n = 1..1000

Formula

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

Example

79 is in the sequence because 79/log(79) - 73/log(73) = 1.065... > 1.

Prog

(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

Crossrefs

Cf. A060770, A060771.

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

Sequence in context: A177873 A234973 A134100 * A355161 A031925 A325058

Adjacent sequences: A060766 A060767 A060768 * A060770 A060771 A060772

Keyword

nonn

Author

Ulrich Schimke (ulrschimke(AT)aol.com)

Status

approved