cp's OEIS Frontend

A383270 Length of the longest sequence of contiguous 1s in the binary expansion of n after flipping at most one 0-bit to 1.

%I A383270 #34 May 07 2025 19:18:45
%S A383270 1,1,2,2,2,3,3,3,2,2,3,4,3,4,4,4,2,2,2,3,3,3,4,5,3,3,4,5,4,5,5,5,2,2,
%T A383270 2,3,2,3,3,4,3,3,3,4,4,4,5,6,3,3,3,3,4,4,5,6,4,4,5,6,5,6,6,6,2,2,2,3,
%U A383270 2,3,3,4,2,2,3,4,3,4,4,5,3,3,3,3,3,3,4,5
%N A383270 Length of the longest sequence of contiguous 1s in the binary expansion of n after flipping at most one 0-bit to 1.
%C A383270 There is only one allowed bit flip from 0 to 1 for each term, unless n is of the form 2^k-1 in which case a(n) = k.
%C A383270 At most one bit flip from 0 to 1 is allowed. If the original binary representation already contains the longest run of 1s, no flip is required.
%F A383270 a(n) <= 1 + floor(log_2(n)).
%F A383270 a(2^k-1) = k.
%F A383270 a(2^k) = 2 for k > 0.
%F A383270 a(2^k+1) = 2.
%F A383270 A038374(n) <= a(n) <= A000120(n)+1. - _Michael S. Branicky_, Apr 21 2025
%e A383270 a(3) = 2 because 3 = 11_2 and there is no need to flip any bit.
%e A383270 a(1775) = 8 because 1775 = 11011101111_2 and if we flip the 7th bit we get 1101111111_2 which has the longest sequence of contiguous 1s of length 8.
%o A383270 (Python)
%o A383270 def a(n):
%o A383270     if n == 0: return 1
%o A383270     if n.bit_length() == n.bit_count(): return n.bit_length()
%o A383270     c = p = m = 0
%o A383270     while n:
%o A383270         if n & 1: c += 1
%o A383270         else:
%o A383270             p = c * ((n & 2) > 0)
%o A383270             c = 0
%o A383270         if (pc := p + c) > m: m = pc
%o A383270         n >>= 1
%o A383270     return m + 1
%o A383270 print([a(n) for n in range(1,88)])
%o A383270 (PARI) a(n) = if (n==0, return(1)); my(b=binary(n), vz = select(x->(x==0), b, 1), m=0); if (#vz <= 1, return (#b)); vz = concat(0, concat(Vec(vz), #b+1)); for (i=1, #vz-2, m = max(m, vz[i+2]-vz[i]-1)); m; \\ _Michel Marcus_, May 02 2025
%Y A383270 Cf. A000079, A000120, A007088, A070939, A038374.
%K A383270 nonn,base
%O A383270 0,3
%A A383270 _Darío Clavijo_, Apr 21 2025