A087118 Numbers having exactly one maximal group of consecutive zeros in binary representation of n.

0, 2, 4, 5, 6, 8, 9, 11, 12, 13, 14, 16, 17, 19, 23, 24, 25, 27, 28, 29, 30, 32, 33, 35, 39, 47, 48, 49, 51, 55, 56, 57, 59, 60, 61, 62, 64, 65, 67, 71, 79, 95, 96, 97, 99, 103, 111, 112, 113, 115, 119, 120, 121, 123, 124, 125, 126, 128, 129, 131, 135, 143, 159, 191

Offset

1,2

Comments

A087116(a(n)) = 1.

a(n) = A043687(n-1) for 1 < n < 1000. - Georg Fischer, Oct 19 2018

Links

Gheorghe Coserea, Table of n, a(n) for n = 1..12343

Index entries for sequences related to binary expansion of n

Formula

From Gheorghe Coserea, Sep 28-30 2015: (Start)

a((n^3 - n)/6 + 2) = 2^n for n >= 1.

a((n^3 - n)/6 + 2 + n) = 2^n + 2^(n-1) for n >= 2.

a((n^3 - n)/6 + 2 + n + n-1) = 2^n + 2^(n-1) + 2^(n-2) for n >= 3.

a(n) < 2*2^((6*n)^(1/3)) and limsup a(n)/2^((6*n)^(1/3)) = 2.

a(n) > 1/2 * 2^((6*n)^(1/3)) for n>=3 and 1/2 <= liminf a(n)/(2^((6*n)^(1/3))) <= 1.

(End)

Maple

0, seq(seq(seq(2^n - 2^b + 2^a - 1, a=0..b-1), b=n-1..1, -1), n=0..10); # Robert Israel, Oct 01 2015

Mathematica

Table[2^n - 2^b + 2^a - 1, {n, 0, 10}, {b, n-1, 1, -1}, {a, 0, b-1}] // Flatten // Prepend[#, 0]& (* Jean-François Alcover, Apr 11 2019, after  Robert Israel *)

Prog

(PARI)
num(a, b, c) = (1 << (a+b+c)) - (1 << (b+c)) + (1 << c)  - 1;
succ(a, b, c) = {
    if (b > 1, return([a, b-1, c+1]));
    if (c > 0, return([a+1, c, 0]));
    return([1, a+1, 0]);
};
seq(n) = {
    my(a = 1, b = 1, c = 0, v = vector(n));
    for (i = 2, n, v[i] = num(a, b, c);
         my(x = succ(a, b, c)); a = x[1]; b = x[2]; c = x[3]);
    return(v);
};
seq(64)  \\ Gheorghe Coserea, Sep 28 2015

Crossrefs

Cf. A007088, A023416, A043687, A087119.

Sequence in context: A288174 A280998 A043687 * A249115 A039032 A000062

Adjacent sequences: A087115 A087116 A087117 * A087119 A087120 A087121

Keyword

nonn

Author

Reinhard Zumkeller, Aug 14 2003

Status

approved