A062530 - OEIS

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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

(list; graph; refs; listen; history; text; internal format)

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.