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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
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.
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
Sequence in context: A064896 A076188 A265852 * A343727 A340559 A073674
KEYWORD
nonn,base
AUTHOR
Rémy Sigrist, May 24 2020
STATUS
approved