A016045 a(n) is the smallest prime p(k) such that the gaps between the primes p(k), p(k+1), p(k+2), ..., p(k+n) are 2, 4, 6, ... 2n.

3, 5, 17, 347, 13901, 128981, 128981, 113575727, 2426256797, 137168442221, 4656625081181, 101951758179851, 484511389338941, 221860944705726407

Offset: 1

Author

Robert G. Wilson v

Keywords

• nonn
• more

Examples

			Consider consecutive primes 347, 349, 353, 359, 367. The gaps are 2, 4, 6, 8, so a(4)=347.
		

References

• Steven Kahan, 2-4-6-8...Prime Gaps That Appreciate, J. Rec. Math., Vol. 25 #1, pp. 44-46, 1993

Crossrefs

Cf. A263049.

Formula

a(n) = min{x : x = prime; {x + k + k^2} = primes following x for k=1, .., n}

Extensions

Corrected and extended by Jud McCranie, Jun 24 2000

a(11)-a(13) from Dmitry Petukhov, Oct 03 2015

a(14) from Dmitry Petukhov, Jul 06 2016