A082862 - OEIS

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

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OFFSET

1,1

COMMENTS

Similar to but not identical to A074327.

LINKS

Table of n, a(n) for n=1..11.

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

Cf. A033844, A051439, A074327.

Sequence in context: A289230 A350568 A249690 * A206948 A089364 A178829

Adjacent sequences: A082859 A082860 A082861 * A082863 A082864 A082865

KEYWORD

nonn,hard,more

AUTHOR

Labos Elemer, Apr 14 2003

EXTENSIONS

Data corrected and extended by Amiram Eldar, Aug 10 2024

STATUS

approved