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

3, 5, 7, 11, 13, 17, 19, 23, 31, 41, 43, 47, 61, 71, 73, 83, 101, 103, 107, 109, 113, 131, 137, 139, 151, 157, 163, 167, 173, 179, 181, 193, 197, 199, 227, 229, 233, 239, 241, 257, 263, 269, 271, 277, 281, 283, 311

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

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

Prog

(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

Crossrefs

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

Sequence in context: A064534 A139758 A306084 * A246568 A338132 A120334

Adjacent sequences: A060767 A060768 A060769 * A060771 A060772 A060773

Keyword

nonn

Author

Ulrich Schimke (ulrschimke(AT)aol.com)

Status

approved