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A335133 Binary interpretation of the left diagonal of the EQ-triangle with first row generated from the binary expansion of n, with most significant bit given by first row. 2
0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 11, 10, 13, 12, 14, 15, 16, 17, 18, 19, 22, 23, 20, 21, 26, 27, 24, 25, 28, 29, 30, 31, 32, 33, 35, 34, 36, 37, 39, 38, 44, 45, 47, 46, 40, 41, 43, 42, 53, 52, 54, 55, 49, 48, 50, 51, 57, 56, 58, 59, 61, 60, 62, 63, 64, 65, 66, 67 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,3

COMMENTS

For any nonnegative number n, the EQ-triangle for n is built by taking as first row the binary expansion of n (without leading zeros), having each entry in the subsequent rows be the EQ of the two values above it (a "1" indicates that these two values are equal, a "0" indicates that these values are different).

This sequence is a self-inverse permutation of the nonnegative numbers.

LINKS

Rémy Sigrist, Table of n, a(n) for n = 0..8192 (n = 0..2^13)

Index entries for sequences related to binary expansion of n

Index entries for sequences that are permutations of the natural numbers

FORMULA

a(floor(n/2)) = floor(a(n)/2).

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

a(2^k) = 2^k for any k >= 0.

a(2^k+1) = 2^k+1 for any k >= 0.

a(2^k-1) = 2^k-1 for any k >= 0.

Apparently, a(n) + A334727(n) = A055010(A070939(n)) for any n > 0.

EXAMPLE

For n = 42:

- the binary representation of 42 is "101010",

- the corresponding EQ-triangle is:

         1 0 1 0 1 0

          0 0 0 0 0

           1 1 1 1

            1 1 1

             1 1

              1

- the bits on the left diagonal are: 1, 0, 1, 1, 1, 1,

- so a(42) = 2^5 + 2^3 + 2^2 + 2^1 + 2^0 = 47.

PROG

(PARI) a(n) = {

    my (b=binary(n), v=0);

    forstep (x=#b-1, 0, -1,

        if (b[1], v+=2^x);

        b=vector(#b-1, k, b[k]==b[k+1])

    );

    return (v)

}

CROSSREFS

Cf. A055010, A070939, A279645, A334727 (XOR variant).

Sequence in context: A239088 A162344 A283962 * A183083 A113220 A113218

Adjacent sequences:  A335130 A335131 A335132 * A335134 A335135 A335136

KEYWORD

nonn,look,base

AUTHOR

Rémy Sigrist, May 24 2020

STATUS

approved

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Last modified August 12 11:16 EDT 2020. Contains 336438 sequences. (Running on oeis4.)