A358259 Positions of the first n-bit number to appear in Van Eck's sequence (A181391).

1, 5, 10, 24, 41, 52, 152, 162, 364, 726, 1150, 2451, 4626, 9847, 18131, 36016, 71709, 143848, 276769, 551730, 1086371, 2158296, 4297353, 8607525, 17159741, 34152001, 68194361, 136211839, 271350906, 541199486, 1084811069, 2165421369, 4331203801, 8643518017, 17303787585

Offset

1,2

Comments

Binary version of the concept behind A358180.

Links

Table of n, a(n) for n=1..35.

Example

First terms written in binary, substituting "." for 0 to enhance the pattern of 1's.
   n      a(n)                   a(n)_2
  -------------------------------------
   1        1                         1
   2        5                       1.1
   3       10                      1.1.
   4       24                     11...
   5       41                    1.1..1
   6       52                    11.1..
   7      152                  1..11...
   8      162                  1.1...1.
   9      364                 1.11.11..
  10      726                1.11.1.11.
  11     1150               1...111111.
  12     2451              1..11..1..11
  13     4626             1..1....1..1.
  14     9847            1..11..111.111
  15    18131           1...11.11.1..11
  16    36016          1...11..1.11....
  17    71709         1...11......111.1
  18   143848        1...11...1111.1...
  19   276769       1....111..1..1....1
  20   551730      1....11.1.11..11..1.
  21  1086371     1....1..1..111.1...11
  22  2158296    1.....111.111.11.11...
  23  4297353   1.....11..1..1.1...1..1
  24  8607525  1.....11.1.1.111..1..1.1
  etc.

Mathematica

nn = 2^20; q[_] = False; q[0] = True; a[_] = 0; c[_] = -1; c[0] = 2; m = 1; {1}~Join~Rest@ Reap[Do[j = c[m]; k = m; c[m] = n; m = 0; If[j > 0, m = n - j]; If[! q[#], Sow[n]; q[#] = True] & @ IntegerLength[k, 2], {n, 3, nn}] ][[-1, -1]]

Prog

(Python)
from itertools import count
def A358259(n):
    b, bdict, k = 0, {0:(1, )}, 1<<n-1 if n > 1 else 0
    for m in count(2):
        if b >= k:
            return m-1
        if len(l := bdict[b]) > 1:
            b = m-1-l[-2]
            if b in bdict:
                bdict[b] = (bdict[b][-1], m)
            else:
                bdict[b] = (m, )
        else:
            b = 0
            bdict[0] = (bdict[0][-1], m) # Chai Wah Wu, Nov 06 2022

Crossrefs

Cf. A181391, A358168, A358180, A358258.

Sequence in context: A237435 A280721 A300552 * A037240 A182095 A177432

Adjacent sequences: A358256 A358257 A358258 * A358260 A358261 A358262

Keyword

nonn,base

Author

Michael De Vlieger, Nov 05 2022

Extensions

a(30)-a(34) from Chai Wah Wu, Nov 06 2022

a(35) from Martin Ehrenstein, Nov 07 2022

Status

approved