A358258 First n-bit number to appear in Van Eck's sequence (A181391).

0, 2, 6, 9, 17, 42, 92, 131, 307, 650, 1024, 2238, 4164, 8226, 17384, 33197, 67167, 133549, 269119, 525974, 1055175, 2111641, 4213053, 8444257, 16783217, 33601813, 67405064, 134239260, 268711604, 538400994, 1076155844, 2152693259, 4299075300, 8594396933, 17203509931

Offset

1,2

Comments

Binary version of A358168.

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        0                         .
   2        2                        1.
   3        6                       11.
   4        9                      1..1
   5       17                     1...1
   6       42                    1.1.1.
   7       92                   1.111..
   8      131                  1.....11
   9      307                 1..11..11
  10      650                1.1...1.1.
  11     1024               1..........
  12     2238              1...1.11111.
  13     4164             1.....1...1..
  14     8226            1.......1...1.
  15    17384           1....11111.1...
  16    33197          1......11.1.11.1
  17    67167         1.....11..1.11111
  18   133549        1.....1..11.1.11.1
  19   269119       1.....11.11..111111
  20   525974      1........11.1..1.11.
  21  1055175     1.......11..111...111
  22  2111641    1.......111...1..11..1
  23  4213053   1.......1..1..1..1111.1
  24  8444257  1.......11.11..1.11....1

Mathematica

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

Prog

(Python)
from itertools import count
def A358258(n):
    b, bdict, k = 0, {0:(1, )}, 1<<n-1 if n > 1 else 0
    for m in count(2):
        if b >= k:
            return b
        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, A358259.

Sequence in context: A054974 A072481 A032471 * A156222 A002886 A028724

Adjacent sequences: A358255 A358256 A358257 * A358259 A358260 A358261

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