A332520 Fixed points of A331364.

0, 1, 2, 3, 4, 5, 8, 10, 12, 15, 16, 17, 32, 34, 48, 51, 64, 68, 80, 85, 128, 136, 160, 170, 192, 204, 240, 255, 256, 257, 512, 514, 768, 771, 1024, 1028, 1280, 1285, 2048, 2056, 2560, 2570, 3072, 3084, 3840, 3855, 4096, 4112, 4352, 4369, 8192, 8224, 8704

Offset

1,3

Comments

These are the numbers with at most one kind of nonzero digit in any base of the form 2^2^k (with k >= 0).

If k belongs to the sequence, then A001196(k) also belongs to the sequence, and conversely.

For any positive term m:

- the number of runs of consecutive 1's in the binary representation of m is a power of 2,

- the runs of consecutive 1's in the binary representation of m have all the same length, a power of 2.

Apparently, for any k >= 0, there are A001316(k) nonzero terms with 1+k binary digits.

Links

Rémy Sigrist, Table of n, a(n) for n = 1..6562

Rémy Sigrist, Binary plot of the terms < 2^2^10

Rémy Sigrist, PARI program for A332520

Example

The first terms, alongside their binary representation, are:
  n   a(n)  bin(a(n))
  --  ----  ---------
   1     0          0
   2     1          1
   3     2         10
   4     3         11
   5     4        100
   6     5        101
   7     8       1000
   8    10       1010
   9    12       1100
  10    15       1111
  11    16      10000
  12    17      10001
  13    32     100000
  14    34     100010
  15    48     110000
  16    51     110011

Prog

(PARI) See Links section.

Crossrefs

Cf. A001196, A001316, A331364.

Sequence in context: A090556 A369152 A223539 * A211544 A325109 A080713

Adjacent sequences: A332517 A332518 A332519 * A332521 A332522 A332523

Keyword

nonn,base

Author

Rémy Sigrist, Jun 24 2020

Status

approved