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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 (list; graph; refs; listen; history; text; internal format)
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^(n-1)]+2^n = Min{p | p-prevprime(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

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Last modified September 26 20:36 EDT 2020. Contains 337374 sequences. (Running on oeis4.)