%I #34 Nov 11 2023 00:15:41
%S 1,3,4,6,8,12,38,24,18,36,48,20,248,588,144,252,5520,168,7200,2400,
%T 2850
%N 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.
%C Similar to A065083 but using binary repdigits instead of base 10.
%C Note that as in A065083, the most significant digit/bit is not replaced with a zero in determining a prime.
%C a(21) > 7800.
%C a(25) = 11520 and a(n) > 12000 for n in 21..24 and n > 25 using A272143. - _Michael S. Branicky_, Nov 09 2023
%e a(3)=6 because 2^6 - 1 = 111111_2 and
%e 1) 111101_2 = 61,
%e 2) 111011_2 = 59,
%e 3) 101111_2 = 47,
%e and no other k < 6 yields exactly three primes.
%o (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
%o (Python)
%o from itertools import count
%o from sympy import isprime
%o def A367081(n):
%o for k in count(1):
%o a, c = (1<<k)-1, 0
%o for i in range(k-2,0,-1):
%o if isprime(a^(1<<i)):
%o c += 1
%o if c >= n+1:
%o break
%o if c == n:
%o return k # _Chai Wah Wu_, Nov 11 2023
%Y Cf. A002275, A034093, A065074, A065083, A272143.
%K nonn,base,more
%O 0,2
%A _Robert Price_, Nov 06 2023