A367186 Numbers that can be written as 2^k + prime in more than one way.

4, 6, 7, 9, 11, 13, 15, 18, 19, 21, 23, 25, 27, 31, 33, 35, 37, 39, 43, 45, 47, 49, 51, 55, 57, 61, 63, 67, 69, 71, 73, 75, 77, 79, 81, 83, 85, 87, 91, 93, 95, 99, 101, 103, 105, 107, 109, 111, 113, 115, 117, 121, 123, 125, 129, 131, 133, 135, 139, 141, 143, 145, 147, 151, 153, 155

Offset: 1

Author

Yuda Chen, Nov 08 2023

Keywords

• nonn

Comments

Numbers m such that A109925(m) > 1.

Examples

			4 is a term since 4 = 2^0 + 3 = 2^1 + 2 which is 2 ways.
6 is a term since 6 = 2^0 + 5 = 2^2 + 2.
		

Crossrefs

Subsequence of A118955.

Cf. A000040, A000079, A109925.

Programs

PARI

isok(m) = sum(k=0, logint(m,2), isprime(m-2^k)) > 1; \\ Michel Marcus, Nov 10 2023

Python

from itertools import count, islice
from sympy import isprime
def A367186_gen(startvalue=1): # generator of terms >= startvalue
    for n in count(max(startvalue,1)):
        c = 0
        for i in range(n.bit_length()-1,-1,-1):
            if isprime(n-(1<1:
                yield n
                break
A367186_list = list(islice(A367186_gen(),30)) # Chai Wah Wu, Nov 29 2023