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A308811 Numbers k such that the binary plot of the list of divisors of k has reflection symmetry. 1
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 (list; graph; refs; listen; history; text; internal format)
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

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Last modified February 16 21:46 EST 2020. Contains 331975 sequences. (Running on oeis4.)