A357305 Numbers k > 1 such that the ratio (numbers of zeros)/(total length) in the binary representation of k^2 is a new minimum.

2, 3, 5, 11, 45, 181, 48589783221, 66537313397, 398064946368587, 796095014224053

Offset

1,1

Links

Table of n, a(n) for n=1..10.

Example

    k    k^2  (binary zeros)/A070939(k^2)
    .      .   .     k^2 written in binary
    2      4  2/3   [1, 0, 0]
    3      9  1/2   [1, 0, 0, 1]
    5     25  2/5   [1, 1, 0, 0, 1]
   11    121  2/7   [1, 1, 1, 1, 0, 0, 1]
   45   2025  3/11  [1, 1, 1, 1, 1, 1, 0, 1, 0, 0, 1]
  181  32761  2/15  [1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 0, 0, 1]

Crossrefs

Cf. A000120, A000290, A070939, A159918, A230097.

Sequence in context: A003686 A086506 A109462 * A000905 A065296 A114895

Adjacent sequences: A357302 A357303 A357304 * A357306 A357307 A357308

Keyword

nonn,base,hard,more

Author

Hugo Pfoertner, Oct 01 2022

Extensions

a(7)-a(8) from Michael S. Branicky, Oct 01 2022 using A230097, verified with exhaustive search Oct 02 2022

a(9)-a(10) from Hugo Pfoertner, Nov 30 2022

Status

approved