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

1, 2, 3, 4, 8, 10, 15, 16, 32, 64, 128, 136, 170, 255, 256, 512, 1024, 2048, 4096, 8192, 16384, 32768, 32896, 34952, 43690, 65535, 65536, 131072, 262144, 524288, 1048576, 2097152, 4194304, 8388608, 16777216, 33554432, 67108864, 134217728

Offset

1,2

Comments

The sequence is infinite as it contains every power of 2 (A000079).

The product of the first five Fermat primes (A019434), 4294967295 = 3 * 5 * 17 * 257 * 65537, is also a member of this sequence.

Every term belongs to A135772.

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).

Links

Table of n, a(n) for n=1..38.

Rémy Sigrist, Binary plot of the first 48 terms

Formula

A295368(a(n)) = a(n).

Example

Regarding 170:
- the divisors of 170 are: 1, 2, 5, 10, 17, 34, 85, 170,
- in binary: "1", "10", "101", "1010", "10001", "100010", "1010101", "10101010",
- the corresponding binary plot is:
  .             1         .             #
    .         1 0           .         #
      .     1 0 1             .     #   #
        . 1 0 1 0               . #   #
        1 0 0 0 1               # .     #
      1 0 0 0 1 0             #     . #
    1 0 1 0 1 0 1           #   #   # . #
  1 0 1 0 1 0 1 0         #   #   #   # .
                  .                       .
                    .                       .
- this binary plot has reflection symmetry,
- hence 170 belongs to this sequence.

Prog

(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)) }

Crossrefs

Cf. A000079, A019434, A135772, A295368.

Sequence in context: A242762 A005542 A037171 * A295296 A186417 A207644

Adjacent sequences: A308808 A308809 A308810 * A308812 A308813 A308814

Keyword

nonn,base

Author

Rémy Sigrist, Jul 08 2019

Status

approved