

A062530


Smallest prime p such that there is a gap of 2^n between p and previous prime.


2



3, 5, 11, 97, 1847, 5623, 89753, 3851587, 1872852203, 1999066711903, 22790428875365903
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OFFSET

0,1


COMMENTS

a(2)=11 because 7 and 11 are consecutive primes with difference 4.  Sascha Kurz, Mar 05 2002
The next two terms are <= 13615411331526592827872074749865096844383295034548454421 and 768784577114627305753353689789300110953010089817032096740065409732504678169114467301254783622575120297131239844 respectively.  Larry Reeves (larryr(AT)acm.org), Jun 13 2002


LINKS

Table of n, a(n) for n=0..10.
T. R. Nicely, List of prime gaps


FORMULA

a(n) = A000230[2^(n1)]+2^n = Min{p  pprevprime(p)=2^n}.  Amarnath Murthy, Feb 24 2002


PROG

(PARI) a(n) = {q = 2; p = nextprime(q+1); gap = 2^n; while(p  q != gap, q = p; p = nextprime(p+1)); p; } \\ Michel Marcus, Dec 26 2013


CROSSREFS

Cf. A062529.
Cf. A000230.
Sequence in context: A232536 A168040 A068157 * A089628 A083841 A277552
Adjacent sequences: A062527 A062528 A062529 * A062531 A062532 A062533


KEYWORD

nonn,hard,more


AUTHOR

Labos Elemer, Jun 25 2001


EXTENSIONS

More terms from Sascha Kurz, Mar 05 2002
Further terms from Larry Reeves (larryr(AT)acm.org), Jun 13 2002
Edited by N. J. A. Sloane Aug 31 2009 at the suggestion of R. J. Mathar


STATUS

approved



