A087118 - OEIS

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

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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]);