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Search: id:A060770
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| A060770 |
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"Early" primes: upper ends of prime gaps that are smaller than the prime number theorem predicts. |
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+0
2
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| 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
(list; graph; listen)
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OFFSET
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1,1
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LINKS
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Harry J. Smith, Table of n, a(n) for n=1,...,1000
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FORMULA
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A prime p belongs to the sequence iff p/log(p) - q/log(q) < 1 where q is the preceding prime
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EXAMPLE
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11 is okay since 11/log(11) - 7/log(7) = 0.990... < 1
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PROGRAM
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(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; ) } [From Harry J. Smith (hjsmithh(AT)sbcglobal.net), Jul 11 2009]
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CROSSREFS
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Apart from 2 this is the complementary prime set to A060769.
Sequence in context: A120637 A064534 A139758 this_sequence A120334 A000978 A128925
Adjacent sequences: A060767 A060768 A060769 this_sequence A060771 A060772 A060773
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KEYWORD
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nonn
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AUTHOR
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Ulrich Schimke (ulrschimke(AT)aol.com)
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