A368844 a(n) gives the number of triples of equally spaced 0's in the binary expansion of n (without leading zeros).

0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 2, 1, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 4, 2, 2, 1, 0, 0, 0, 0, 2, 0, 1, 0, 0, 0, 0, 0, 2, 1, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 6, 4, 3, 2, 2, 2, 1, 1, 2, 0, 1, 0, 0, 0, 0, 0, 3, 2, 0, 0, 1, 1, 0

Offset

0,17

Links

Table of n, a(n) for n=0..86.

Index entries for sequences related to binary expansion of n

Formula

a(2*n) >= a(n).

a(2*n + 1) = a(n).

Example

For n = 277:
- the binary expansion of 277 is "100010101",
- we have the following triples:   000
                                   0 0 0
                                     0 0 0
- so a(277) = 3.

Prog

(PARI) a(n, t = 0, base = 2) = { my (d = digits(n, base), v = 0); for (i = 1, #d-2, if (d[i]==t, forstep (j = i+2, #d, 2, if (d[i]==d[j] && d[i]==d[(i+j)/2], v++; ); ); ); ); return (v); }
(Python)
def A368844(n):
    l = len(s:=bin(n)[3:])
    return sum(1 for i in range(l-2) for j in range(1, l-i+1>>1) if s[i:i+(j<<1)+1:j]=='000') # Chai Wah Wu, Jan 10 2024

Crossrefs

Cf. A368842, A368843.

Sequence in context: A010109 A304021 A056974 * A181563 A056976 A279281

Adjacent sequences: A368841 A368842 A368843 * A368845 A368846 A368847

Keyword

nonn,base,easy

Author

Rémy Sigrist, Jan 07 2024

Status

approved