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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.
9
2, 19, 131, 311, 1619, 3671, 1742537, 148948139, 2777105129, 16149760533341, 10082409897709157
OFFSET
1,1
COMMENTS
Similar to but not identical to A074327.
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]
EXAMPLE
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... .
MATHEMATICA
q=4; Do[s=(Prime[2^n+1]-Prime[2^n])/Log[Prime[2^n]]//N; If[s<q, Print[{Prime[2^n], s}]; q=s], {n, 0, 30}] (* corrected by Amiram Eldar, Aug 10 2024 *)
CROSSREFS
KEYWORD
nonn,hard,more
AUTHOR
Labos Elemer, Apr 14 2003
EXTENSIONS
Data corrected and extended by Amiram Eldar, Aug 10 2024
STATUS
approved