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A087118 Numbers having exactly one maximal group of consecutive zeros in binary representation of n. 4
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 (list; graph; refs; listen; history; text; internal format)
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-Fran├žois 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

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Last modified November 29 02:45 EST 2020. Contains 338756 sequences. (Running on oeis4.)