A057196 Numbers k such that 2^k + 9 is prime.

1, 2, 3, 5, 6, 7, 9, 10, 18, 23, 30, 37, 47, 57, 66, 82, 95, 119, 175, 263, 295, 317, 319, 327, 670, 697, 886, 1342, 1717, 1855, 2394, 2710, 3229, 3253, 3749, 4375, 4494, 4557, 5278, 5567, 9327, 10129, 12727, 13615, 14893, 16473, 23639, 40053, 44399, 50335, 80949

Offset: 1

Author

Robert G. Wilson v, Sep 15 2000

Keywords

• nonn

Comments

Some of the larger terms are only probable primes.

For these numbers k, 2^(k-1)*(2^k+9) has deficiency 10 (see A101223). - M. F. Hasler, Jul 18 2016

The terms a(48)-a(51) were found by Mike Oakes, a(52) found by Gary Barnes, and a(53-56) found by Lelio R Paula (see link Henri Lifchitz and Renaud Lifchitz). - Elmo R. Oliveira, Dec 01 2023

Examples

			For k = 10, 2^10 + 9 = 1033 is prime.
For k = 30, 2^30 + 9 = 1073741833 is prime.
		

Links

• Robert Price, Table of n, a(n) for n = 1..56
• Keith Conrad, Square patterns and infinitude of primes, University of Connecticut, 2019.
• Henri Lifchitz and Renaud Lifchitz (Editors), Search for 2^n+9, PRP Top Records.

Crossrefs

Cf. A094076, A101223, A104070 (primes of the form 2^k+9). [Klaus Brockhaus, Mar 14 2009]

Cf. A019434 (primes 2^k+1), A057732 (2^k+3), A059242 (2^k+5), A057195 (2^k+7), this sequence (2^k+9), A102633 (2^k+11), A102634 (2^k+13), A057197 (2^k+15), A057200 (2^k+17), A057221 (2^k+19), A057201 (2^k+21), A057203 (2^k+23). [M. F. Hasler, Jul 18 2016]

Programs

Mathematica

Do[ If[ PrimeQ[ 2^n +9 ], Print[n]], { n, 1, 15000 }]

PARI

for(n=1, oo, ispseudoprime(2^n+9)&&print1(n", ")) \\ M. F. Hasler, Jul 18 2016

Extensions

a(48)-a(51) from Mike Oakes, Aug 17 2001

Edited by T. D. Noe, Oct 30 2008