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

Author

Michael De Vlieger, Nov 05 2022

Keywords

• nonn
• base

Comments

Binary version of A358168.

Examples

			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
		

Crossrefs

Cf. A181391, A358168, A358180, A358259.

Programs

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]]

Python

from itertools import count
def A358258(n):
    b, bdict, k = 0, {0:(1,)},1< 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

Extensions

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

a(35) from Martin Ehrenstein, Nov 07 2022