A367081 The least k such that exactly n binary near-repunit primes can be formed from 2^k-1 by changing one digit from 1 to 0.

1, 3, 4, 6, 8, 12, 38, 24, 18, 36, 48, 20, 248, 588, 144, 252, 5520, 168, 7200, 2400, 2850

Offset

0,2

Comments

Similar to A065083 but using binary repdigits instead of base 10.

Note that as in A065083, the most significant digit/bit is not replaced with a zero in determining a prime.

a(21) > 7800.

a(25) = 11520 and a(n) > 12000 for n in 21..24 and n > 25 using A272143. - Michael S. Branicky, Nov 09 2023

Links

Table of n, a(n) for n=0..20.

Example

a(3)=6 because 2^6 - 1 = 111111_2 and
                      1) 111101_2 = 61,
                      2) 111011_2 = 59,
                      3) 101111_2 = 47,
and no other k < 6 yields exactly three primes.

Prog

(PARI) a(n) = my(k=1); while(sum(i=1, k-2, ispseudoprime(2^k-1-2^i)) != n, k++); k \\ Thomas Scheuerle, Nov 07 2023
(Python)
from itertools import count
from sympy import isprime
def A367081(n):
    for k in count(1):
        a, c = (1<<k)-1, 0
        for i in range(k-2, 0, -1):
            if isprime(a^(1<<i)):
                c += 1
            if c >= n+1:
                break
        if c == n:
            return k # Chai Wah Wu, Nov 11 2023

Crossrefs

Cf. A002275, A034093, A065074, A065083, A272143.

Sequence in context: A146566 A204658 A139041 * A244607 A136483 A240494

Adjacent sequences: A367078 A367079 A367080 * A367082 A367083 A367084

Keyword

nonn,base,more

Author

Robert Price, Nov 06 2023

Status

approved