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

%I #17 Nov 05 2024 19:07:45

%S 3,5,11,97,1847,5623,89753,3851587,1872852203,1999066711903,

%T 22790428875365903,5333419265419188034369535864127397,

%U 55128448018333565337014555712123010955456071077000028555991473847

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

%C The next two terms are <= 13615411331526592827872074749865096844383295034548454421 and 768784577114627305753353689789300110953010089817032096740065409732504678169114467301254783622575120297131239844 respectively. - Larry Reeves (larryr(AT)acm.org), Jun 13 2002

%H Thomas R. Nicely, <a href="https://faculty.lynchburg.edu/~nicely/gaps/gaplist.html">First occurrence prime gaps</a>. [For local copy see A000101]

%F a(n) = A000230(2^(n-1)) + 2^n = Min{p | p-prevprime(p) = 2^n}. - _Amarnath Murthy_, Feb 24 2002

%F a(n) = A151800(A062529(n)). - _Amiram Eldar_, Nov 04 2024

%e a(2) = 11 because 7 and 11 are consecutive primes with difference 4. - _Sascha Kurz_, Mar 05 2002

%o (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

%Y Cf. A000230, A062529, A151800.

%K nonn,hard,more

%O 0,1

%A _Labos Elemer_, Jun 25 2001

%E More terms from _Sascha Kurz_, Mar 05 2002

%E Further terms from Larry Reeves (larryr(AT)acm.org), Jun 13 2002

%E Edited by _N. J. A. Sloane_ Aug 31 2009 at the suggestion of _R. J. Mathar_

%E a(11)-a(12) calculated from the data at A062529 by _Amiram Eldar_, Nov 04 2024