A368843 a(n) gives the number of triples of equally spaced 1's in the binary expansion of n.

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

Offset

0,16

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:  1   1   1
                                      1 1 1
- so a(277) = 2.

Prog

(PARI) a(n, t = 1, 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 A368843(n):
    l = len(s:=bin(n)[2:])
    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]=='111') # Chai Wah Wu, Jan 10 2024

Crossrefs

Cf. A368842, A368844.

Sequence in context: A249856 A086012 A248394 * A127268 A252459 A083918

Adjacent sequences: A368840 A368841 A368842 * A368844 A368845 A368846

Keyword

nonn,base,easy

Author

Rémy Sigrist, Jan 07 2024

Status

approved