cp's OEIS Frontend

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.

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