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A335132 Numbers whose binary expansion generates 3-fold rotationally symmetric EQ-triangles. 1
0, 1, 3, 5, 7, 9, 15, 17, 31, 33, 63, 65, 73, 119, 127, 129, 255, 257, 297, 349, 373, 395, 419, 471, 511, 513, 585, 653, 709, 827, 883, 951, 1023, 1025, 1193, 1879, 2047, 2049, 2145, 2225, 2257, 3887, 3919, 3999, 4095, 4097, 4321, 4681, 4777, 5501, 5533, 5941 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,3

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).

The second row in such a triangle has binary expansion given by A279645.

If m belongs to this sequence, then A030101(m) also belongs to this sequence.

All positive terms are odd.

This sequence is a variant of A334556; here we use bitwise EQ, there bitwise XOR.

LINKS

Table of n, a(n) for n=1..52.

Rémy Sigrist, Illustration of initial terms

Wikipedia, Logical equality

Index entries for sequences related to binary expansion of n

EXAMPLE

For 349:

- the binary expansion of 349 is "101011101",

- the corresponding EQ-triangle is (with dots instead of 0's for clarity):

     1 . 1 . 1 1 1 . 1

      . . . . 1 1 . .

       1 1 1 . 1 . 1

        1 1 . . . .

         1 . 1 1 1

          . . 1 1

           1 . 1

            . .

             1

- this triangle has 3-fold rotational symmetry, so 349 belongs to this sequence.

PROG

(PARI) is(n) = {

    my (b=binary(n), p=b);

    for (k=1, #b,

        if (b[k]!=p[#p], return (0));

        if (p[1]!=b[#b+1-k], return (0));

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

    );

    return (1);

}

CROSSREFS

Cf. A279645, A334556.

Sequence in context: A064896 A076188 A265852 * A073674 A084722 A083566

Adjacent sequences:  A335129 A335130 A335131 * A335133 A335134 A335135

KEYWORD

nonn,base

AUTHOR

Rémy Sigrist, May 24 2020

STATUS

approved

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Last modified September 18 19:19 EDT 2020. Contains 337172 sequences. (Running on oeis4.)