A368214 Primes with a single 0-bit in binary expansion such that changing the position of the 0-bit always gives a nonprime (including the one with a leading zero).

2, 2039, 6143, 522239, 33546239, 260046847, 16911433727, 32212254719, 2196875771903, 140735340871679, 2251799813685119, 9005000231485439, 576460752169205759, 36893488147410714623, 147573811852188057599, 9444732965739282038783, 154742504910672534362390399

Offset

1,1

Comments

It seems that most of the terms end with '9', followed by those ending with '3', '7', and '1'.

Links

Table of n, a(n) for n=1..17.

Example

2 is a term because 2 is a prime with one '0' in binary form ('10') and '01' is not a prime. 2039 is a term because 2039 is a prime with one '0' in binary form ('11111110111') and changing the position of the '0', for example, '11111111011' = 2043 and '01111111111' = 1023, always results in a composite.

Prog

(Python)
from sympy import isprime
for n in range(1, 100):
    s = n*'1'; c = 0
    for j in range(n+1):
        num = int(s[:j]+'0'+s[j:], 2)
        if isprime(num):
            c += 1
            if c == 1: r = num
            if c == 2: break
    if c == 1: print(r, end = ', ')

Crossrefs

Subsequence of A095078.

Cf. A039986, A081118, A095058, A138290, A208083.

Sequence in context: A125635 A124361 A166339 * A024034 A101722 A004908

Adjacent sequences: A368211 A368212 A368213 * A368215 A368216 A368217

Keyword

base,nonn

Author

Ya-Ping Lu, Dec 23 2023

Status

approved