A086979 Increasing peaks in the prime gap sequence A038664.

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

Offset

1,1

Comments

a(n) is Pi(p_k), 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. Springer-Verlag, 1991, p. 144.

Links

Table of n, a(n) for n=1..29.

Thomas R. Nicely, First occurrence prime gaps [For local copy see A000101]

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