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A335132 Numbers whose binary expansion generates 3-fold rotationally symmetric EQ-triangles.

%I A335132 #7 May 27 2020 01:57:14
%S A335132 0,1,3,5,7,9,15,17,31,33,63,65,73,119,127,129,255,257,297,349,373,395,
%T A335132 419,471,511,513,585,653,709,827,883,951,1023,1025,1193,1879,2047,
%U A335132 2049,2145,2225,2257,3887,3919,3999,4095,4097,4321,4681,4777,5501,5533,5941
%N A335132 Numbers whose binary expansion generates 3-fold rotationally symmetric EQ-triangles.
%C A335132 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).
%C A335132 The second row in such a triangle has binary expansion given by A279645.
%C A335132 If m belongs to this sequence, then A030101(m) also belongs to this sequence.
%C A335132 All positive terms are odd.
%C A335132 This sequence is a variant of A334556; here we use bitwise EQ, there bitwise XOR.
%H A335132 Rémy Sigrist, <a href="/A335132/a335132.png">Illustration of initial terms</a>
%H A335132 Wikipedia, <a href="https://en.wikipedia.org/wiki/Logical_equality#Definition">Logical equality</a>
%H A335132 <a href="/index/Bi#binary">Index entries for sequences related to binary expansion of n</a>
%e A335132 For 349:
%e A335132 - the binary expansion of 349 is "101011101",
%e A335132 - the corresponding EQ-triangle is (with dots instead of 0's for clarity):
%e A335132      1 . 1 . 1 1 1 . 1
%e A335132       . . . . 1 1 . .
%e A335132        1 1 1 . 1 . 1
%e A335132         1 1 . . . .
%e A335132          1 . 1 1 1
%e A335132           . . 1 1
%e A335132            1 . 1
%e A335132             . .
%e A335132              1
%e A335132 - this triangle has 3-fold rotational symmetry, so 349 belongs to this sequence.
%o A335132 (PARI) is(n) = {
%o A335132     my (b=binary(n), p=b);
%o A335132     for (k=1, #b,
%o A335132         if (b[k]!=p[#p], return (0));
%o A335132         if (p[1]!=b[#b+1-k], return (0));
%o A335132         p = vector(#p-1, k, p[k]==p[k+1]);
%o A335132     );
%o A335132     return (1);
%o A335132 }
%Y A335132 Cf. A279645, A334556.
%K A335132 nonn,base
%O A335132 1,3
%A A335132 _Rémy Sigrist_, May 24 2020