cp's OEIS Frontend

A308811 Numbers k such that the binary plot of the list of divisors of k has reflection symmetry.

%I A308811 #54 Jul 28 2019 21:46:24
%S A308811 1,2,3,4,8,10,15,16,32,64,128,136,170,255,256,512,1024,2048,4096,8192,
%T A308811 16384,32768,32896,34952,43690,65535,65536,131072,262144,524288,
%U A308811 1048576,2097152,4194304,8388608,16777216,33554432,67108864,134217728
%N A308811 Numbers k such that the binary plot of the list of divisors of k has reflection symmetry.
%C A308811 The sequence is infinite as it contains every power of 2 (A000079).
%C A308811 The product of the first five Fermat primes (A019434), 4294967295 = 3 * 5 * 17 * 257 * 65537, is also a member of this sequence.
%C A308811 Every term belongs to A135772.
%C A308811 The first 48 terms are all of the form Sum_{i=1..t} 2^(k*t-1) for some k > 0 and t > 0 (see binary plot in Links section).
%H A308811 Rémy Sigrist, <a href="/A308811/a308811.png">Binary plot of the first 48 terms</a>
%F A308811 A295368(a(n)) = a(n).
%e A308811 Regarding 170:
%e A308811 - the divisors of 170 are: 1, 2, 5, 10, 17, 34, 85, 170,
%e A308811 - in binary: "1", "10", "101", "1010", "10001", "100010", "1010101", "10101010",
%e A308811 - the corresponding binary plot is:
%e A308811   .             1         .             #
%e A308811     .         1 0           .         #
%e A308811       .     1 0 1             .     #   #
%e A308811         . 1 0 1 0               . #   #
%e A308811         1 0 0 0 1               # .     #
%e A308811       1 0 0 0 1 0             #     . #
%e A308811     1 0 1 0 1 0 1           #   #   # . #
%e A308811   1 0 1 0 1 0 1 0         #   #   #   # .
%e A308811                   .                       .
%e A308811                     .                       .
%e A308811 - this binary plot has reflection symmetry,
%e A308811 - hence 170 belongs to this sequence.
%o A308811 (PARI) is(n) = { my (d=Vecrev(divisors(n))); if (#binary(d[1])==#d, for (b=0, #d-1, my (t=0); for (i=1, #d, if (bittest(d[i], b), t+=2^(i-1))); if (t!=d[b+1], return (0))); return (1), return (0)) }
%Y A308811 Cf. A000079, A019434, A135772, A295368.
%K A308811 nonn,base
%O A308811 1,2
%A A308811 _Rémy Sigrist_, Jul 08 2019