

A086979


Increasing peaks in the prime gap sequence A038664.


4



46, 282, 738, 3302, 7970, 8028, 14862, 15783, 34202, 44773, 44903, 85787, 110224, 165326, 402884, 460883, 474029, 786922, 887313, 2959782, 4875380, 8321465, 9330121, 20226285, 45808557, 92276646, 114867712, 201745031, 265878477
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OFFSET

1,1


COMMENTS

a(n) is Pi(p_k) the count of the number of primes up to and including p_k, where p_k is the initial prime of a prime gap g = p_k+1  p_k. All even gaps smaller than g occur at a smaller prime and the next even gap g+2 also occurs earlier.


REFERENCES

P. Ribenboim, The Little Book of Big Primes. SpringerVerlag, 1991, p. 144.


LINKS

Table of n, a(n) for n=1..29.
T. R. Nicely, List of "First occurrence prime gaps"
Eric Weisstein's World of Mathematics, Prime Gaps.


EXAMPLE

282 is in this list because the 282nd prime is 1831, the next prime
is 1847, giving a prime gap of 16. All even gaps less than 16 occur
before this (for smaller primes) and the next even gap, 18, also
occurs earlier.


CROSSREFS

Cf. A000230, A001223, A001632, A002386, A038664, A086977, A086978, A086980.
Sequence in context: A026913 A244744 A156841 * A289274 A296402 A077734
Adjacent sequences: A086976 A086977 A086978 * A086980 A086981 A086982


KEYWORD

nonn


AUTHOR

Harry J. Smith, Jul 26 2003


STATUS

approved



