A356421 Positive integers k such that k + p is a power of 2, where p is the least prime greater than k.

3, 15, 61, 255, 2043, 4093, 32765, 65535, 262141, 8388599, 33554397, 134217699, 268435453, 1073741821, 17179869159, 137438953463, 274877906937, 1099511627761, 8796093022179, 17592186044409, 70368744177649, 140737488355323, 281474976710635, 562949953421243

Offset

1,1

Comments

The corresponding sequence of primes is the intersection of A014210 and A356434 without the initial 2.

Links

Table of n, a(n) for n=1..24.

Example

3 + 5 = 8;
15 + 17 = 32;
61 + 67 = 128.

Prog

(Python)
from itertools import islice
from sympy import nextprime
def A356421_gen():
    m = 1
    while True:
        n = m+1<<1
        k = m
        p = nextprime(k)
        while k+p>n:
            k -=1
            p = nextprime(k)
        if k+p==n:
            yield k
        m = n-1
A356421_list = list(islice(A356421_gen(), 30)) # Chai Wah Wu, Sep 11 2022

Crossrefs

Cf. A000040, A000079, A014210, A356434.

Sequence in context: A292483 A218227 A072336 * A122671 A317181 A067562

Adjacent sequences: A356418 A356419 A356420 * A356422 A356423 A356424

Keyword

nonn

Author

Ali Sada, Aug 06 2022

Extensions

Terms from Tom Duff via Seqfan.

Status

approved