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%I #21 Nov 07 2022 02:10:12
%S 0,2,6,9,17,42,92,131,307,650,1024,2238,4164,8226,17384,33197,67167,
%T 133549,269119,525974,1055175,2111641,4213053,8444257,16783217,
%U 33601813,67405064,134239260,268711604,538400994,1076155844,2152693259,4299075300,8594396933,17203509931
%N First n-bit number to appear in Van Eck's sequence (A181391).
%C Binary version of A358168.
%e First terms written in binary, substituting "." for 0 to enhance the pattern of 1's.
%e n a(n) a(n)_2
%e -------------------------------------
%e 1 0 .
%e 2 2 1.
%e 3 6 11.
%e 4 9 1..1
%e 5 17 1...1
%e 6 42 1.1.1.
%e 7 92 1.111..
%e 8 131 1.....11
%e 9 307 1..11..11
%e 10 650 1.1...1.1.
%e 11 1024 1..........
%e 12 2238 1...1.11111.
%e 13 4164 1.....1...1..
%e 14 8226 1.......1...1.
%e 15 17384 1....11111.1...
%e 16 33197 1......11.1.11.1
%e 17 67167 1.....11..1.11111
%e 18 133549 1.....1..11.1.11.1
%e 19 269119 1.....11.11..111111
%e 20 525974 1........11.1..1.11.
%e 21 1055175 1.......11..111...111
%e 22 2111641 1.......111...1..11..1
%e 23 4213053 1.......1..1..1..1111.1
%e 24 8444257 1.......11.11..1.11....1
%t 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]]
%o (Python)
%o from itertools import count
%o def A358258(n):
%o b, bdict, k = 0, {0:(1,)},1<<n-1 if n > 1 else 0
%o for m in count(2):
%o if b >= k:
%o return b
%o if len(l := bdict[b]) > 1:
%o b = m-1-l[-2]
%o if b in bdict:
%o bdict[b] = (bdict[b][-1],m)
%o else:
%o bdict[b] = (m,)
%o else:
%o b = 0
%o bdict[0] = (bdict[0][-1],m) # _Chai Wah Wu_, Nov 06 2022
%Y Cf. A181391, A358168, A358180, A358259.
%K nonn,base
%O 1,2
%A _Michael De Vlieger_, Nov 05 2022
%E a(30)-a(34) from _Chai Wah Wu_, Nov 06 2022
%E a(35) from _Martin Ehrenstein_, Nov 07 2022