A082862 Prime(2^j) where j are the positions at which (prime(2^k+1)-prime(2^k))/log(prime(2^k)) set low-value records.

2, 19, 131, 311, 1619, 3671, 1742537, 148948139, 2777105129, 16149760533341, 10082409897709157

Offset: 1

Author

Labos Elemer, Apr 14 2003

Keywords

• nonn
• hard
• more

Comments

Similar to but not identical to A074327.

Examples

			The values of quotients at primes of this sequence are as follows: 1.442695..., 1.358493..., 1.230719..., 0.348444..., 0.270651..., 0.243658..., 0.139170..., 0.106274..., 0.091976..., 0.065761..., 0.054274... .
		

Links

• American Institute of Mathematics, San Jose State Math Researcher Experiences Epiphany at American Institute Of Mathematics, March 21, 2003. [Wayback Machine link]
• American Institute of Mathematics, Small gaps between consecutive primes. [Wayback Machine link]
• American Institute of Mathematics, On the error in Goldston and Yildirim's "Small gaps between consecutive primes". [Wayback Machine link]

Crossrefs

Cf. A033844, A051439, A074327.

Programs

Mathematica

q=4; Do[s=(Prime[2^n+1]-Prime[2^n])/Log[Prime[2^n]]//N; If[sAmiram Eldar, Aug 10 2024 *)

Extensions

Data corrected and extended by Amiram Eldar, Aug 10 2024