A062530 Smallest prime p such that there is a gap of 2^n between p and previous prime.

3, 5, 11, 97, 1847, 5623, 89753, 3851587, 1872852203, 1999066711903, 22790428875365903, 5333419265419188034369535864127397, 55128448018333565337014555712123010955456071077000028555991473847

Offset

0,1

Comments

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..12.

Thomas R. Nicely, First occurrence prime gaps. [For local copy see A000101]

Formula

a(n) = A000230(2^(n-1)) + 2^n = Min{p | p-prevprime(p) = 2^n}. - Amarnath Murthy, Feb 24 2002

a(n) = A151800(A062529(n)). - Amiram Eldar, Nov 04 2024

Example

a(2) = 11 because 7 and 11 are consecutive primes with difference 4. - Sascha Kurz, Mar 05 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. A000230, A062529, A151800.

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

a(11)-a(12) calculated from the data at A062529 by Amiram Eldar, Nov 04 2024

Status

approved