A072180 Numbers k such that 2^k - k^2 is prime.

5, 7, 9, 17, 19, 51, 53, 81, 83, 119, 189, 219, 227, 301, 455, 461, 623, 2037, 2221, 2455, 3547, 5515, 6825, 8303, 9029, 12103, 49989, 55525, 64773, 80307, 119087, 141915, 192023, 205933, 301683, 307407

Offset

1,1

Comments

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

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

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

Henri Lifchitz found the terms > 40000 in 2001 and 119087 in March 2002. - Hugo Pfoertner, Nov 16 2004

Links

Table of n, a(n) for n=1..36.

Henri Lifchitz, Renaud Lifchitz, PRP Top Records 2^n-n^2.

Mathematica

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

Prog

(PARI) is(n)=isprime(2^n-n^2) \\ Charles R Greathouse IV, Feb 17 2017

Crossrefs

Cf. A024012, A064539, A075896, A072164.

Sequence in context: A294908 A036708 A124822 * A162848 A259359 A024571

Adjacent sequences: A072177 A072178 A072179 * A072181 A072182 A072183

Keyword

hard,nonn

Author

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

Extensions

Edited and extended by Robert G. Wilson v, Jul 01 2002

More terms from Hugo Pfoertner, Nov 16 2004

More terms from Henri Lifchitz submitted by Ray Chandler, Mar 02 2007

Status

approved