A356826 Numbers k such that 2^k - 29 is prime.

5, 8, 104, 212, 79316, 102272, 225536, 340688

Offset: 1

Author

Craig J. Beisel, Aug 29 2022

Keywords

• nonn
• more

Comments

A particularly low-density pseudo-Mersenne sequence. I have verified that there are no additional terms for k < 5*10^4. For k = a(5), a(6), a(7), and a(8), 2^k - 29 is a probable prime (see link).

The terms a(5)-a(8) were discovered by Henri Lifchitz (see link). - Elmo R. Oliveira, Nov 29 2023

Empirically: except for 5, all terms are even. - Elmo R. Oliveira, Nov 29 2023

Examples

			5 is a term because 2^5 - 29 = 3 is prime.
8 is a term because 2^8 - 29 = 227 is prime.
		

Links

• Henri Lifchitz and Renaud Lifchitz, Search for 2^n-29, PRP Top Records.

Crossrefs

Cf. A096502.

Cf. Sequences of numbers k such that 2^k - d is prime: A000043 (d=1), A050414 (d=3), A059608 (d=5), A059609 (d=7), A059610 (d=9), A096817 (d=11), A096818 (d=13), A059612 (d=15), A059611 (d=17), A096819 (d=19), A096820 (d=21), A057220 (d=23), this sequence (d=29).

Programs

PARI

for(n=2, 1000, if(isprime(2^n-29), print1(n, ", ")))