

A335132


Numbers whose binary expansion generates 3fold rotationally symmetric EQtriangles.


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
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OFFSET

1,3


COMMENTS

For any nonnegative number n, the EQtriangle 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 EQtriangle 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 3fold 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+1k], return (0));
p = vector(#p1, 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



