A072180 - OEIS

%I #16 Jun 07 2021 04:50:57

%S 5,7,9,17,19,51,53,81,83,119,189,219,227,301,455,461,623,2037,2221,

%T 2455,3547,5515,6825,8303,9029,12103,49989,55525,64773,80307,119087,

%U 141915,192023,205933,301683,307407

%N Numbers k such that 2^k - k^2 is prime.

%C The numbers corresponding to k = 2037, 2221, 3547 and 5515 have been certified prime with Primo. - _Rick L. Shepherd_, Nov 10 2002

%C The remaining k's > 1000 correspond only to probable primes.

%C Certainly k must be odd. Let N(k) = 2^k - k^2. Additional restrictions come from the facts that 7 | N(k) if k is in {2, 4, 5, 6, 10, 15} mod 21 and 17 | N(k) if k is in {31, 57, 61, 71, 107, 109, 113, 131} mod 136. - Daniel Gronau, Jul 06 2002

%C _Henri Lifchitz_ found the terms > 40000 in 2001 and 119087 in March 2002. - _Hugo Pfoertner_, Nov 16 2004

%H Henri Lifchitz, Renaud Lifchitz, <a href="http://www.primenumbers.net/prptop/searchform.php?form=2%5En-n%5E2">PRP Top Records</a> 2^n-n^2.

%t Do[ If[ PrimeQ[ 2^n - n^2], Print[n]], {n, 1, 22850, 2}]

%o (PARI) is(n)=isprime(2^n-n^2) \\ _Charles R Greathouse IV_, Feb 17 2017

%Y Cf. A024012, A064539, A075896, A072164.

%K hard,nonn

%O 1,1

%A Daniel Gronau (Daniel.Gronau(AT)gmx.de), Jun 30 2002

%E Edited and extended by _Robert G. Wilson v_, Jul 01 2002

%E More terms from _Hugo Pfoertner_, Nov 16 2004

%E More terms from _Henri Lifchitz_ submitted by _Ray Chandler_, Mar 02 2007