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

Author

Harry J. Smith, Jul 26 2003

Keywords

• nonn

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.

Examples

			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.
		

References

• P. Ribenboim, The Little Book of Big Primes. Springer-Verlag, 1991, p. 144.

Links

• Thomas R. Nicely, First occurrence prime gaps [For local copy see A000101]
• Eric Weisstein's World of Mathematics, Prime Gaps.

Crossrefs

Cf. A000230, A001223, A001632, A002386, A038664, A086977, A086978, A086980.