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

1,1

Comments

Numbers m such that A109925(m) > 1.

Links

Table of n, a(n) for n=1..66.

Example

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.

Prog

(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<<i)):
                c+=1
            if c>1:
                yield n
                break
A367186_list = list(islice(A367186_gen(), 30)) # Chai Wah Wu, Nov 29 2023

Crossrefs

Subsequence of A118955.

Cf. A000040, A000079, A109925.

Sequence in context: A186497 A193627 A256792 * A345665 A343177 A085817

Adjacent sequences: A367183 A367184 A367185 * A367187 A367188 A367189

Keyword

nonn

Author

Yuda Chen, Nov 08 2023

Status

approved