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
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
Programs
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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]]
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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
Comments