A059610 Numbers k such that 2^k - 9 is prime.

4, 5, 9, 11, 17, 21, 33, 125, 141, 243, 251, 285, 321, 537, 563, 699, 729, 2841, 3365, 8451, 8577, 9699, 9725, 21011, 22689, 33921, 51761, 655845, 676761, 3480081

Offset: 1

Author

Andrey V. Kulsha, Feb 02 2001

Keywords

• nonn
• more

Comments

Except the first term 4, all terms are odd since 2^(2*m) - 9 = (2^m - 3)*(2^m + 3) is not prime for m > 2.

Examples

			243 is in the sequence because 2^243 - 9 is prime.
		

Links

• 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. Sequences of numbers k such that 2^k - d is prime: A000043 (d=1), A050414 (d=3), A059608 (d=5), A059609 (d=7), this sequence (d=9), A096817 (d=11), A096818 (d=13), A059612 (d=15), A059611 (d=17), A096819 (d=19), A096820 (d=21), A057220 (d=23), A356826 (d=29).

Programs

Mathematica

Select[Range[3,20000],PrimeQ[2^#-9]&] (* Vladimir Joseph Stephan Orlovsky, Feb 26 2011 *)

PARI

is(n)=isprime(2^n-9) \\ Charles R Greathouse IV, Feb 17 2017

Extensions

a(24)-a(25) from Max Alekseyev, a(26)-a(27) from Paul Underwood, added by Max Alekseyev, Feb 09 2012

a(28)-a(29) from Robert Price, Jan 25 2017

a(30) found by Stefano Morozzi, added by Elmo R. Oliveira, Nov 17 2023