This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.
%I A358259 #21 Nov 07 2022 02:10:07
%S A358259 1,5,10,24,41,52,152,162,364,726,1150,2451,4626,9847,18131,36016,
%T A358259 71709,143848,276769,551730,1086371,2158296,4297353,8607525,17159741,
%U A358259 34152001,68194361,136211839,271350906,541199486,1084811069,2165421369,4331203801,8643518017,17303787585
%N A358259 Positions of the first n-bit number to appear in Van Eck's sequence (A181391).
%C A358259 Binary version of the concept behind A358180.
%e A358259 First terms written in binary, substituting "." for 0 to enhance the pattern of 1's.
%e A358259 n a(n) a(n)_2
%e A358259 -------------------------------------
%e A358259 1 1 1
%e A358259 2 5 1.1
%e A358259 3 10 1.1.
%e A358259 4 24 11...
%e A358259 5 41 1.1..1
%e A358259 6 52 11.1..
%e A358259 7 152 1..11...
%e A358259 8 162 1.1...1.
%e A358259 9 364 1.11.11..
%e A358259 10 726 1.11.1.11.
%e A358259 11 1150 1...111111.
%e A358259 12 2451 1..11..1..11
%e A358259 13 4626 1..1....1..1.
%e A358259 14 9847 1..11..111.111
%e A358259 15 18131 1...11.11.1..11
%e A358259 16 36016 1...11..1.11....
%e A358259 17 71709 1...11......111.1
%e A358259 18 143848 1...11...1111.1...
%e A358259 19 276769 1....111..1..1....1
%e A358259 20 551730 1....11.1.11..11..1.
%e A358259 21 1086371 1....1..1..111.1...11
%e A358259 22 2158296 1.....111.111.11.11...
%e A358259 23 4297353 1.....11..1..1.1...1..1
%e A358259 24 8607525 1.....11.1.1.111..1..1.1
%e A358259 etc.
%t A358259 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]]
%o A358259 (Python)
%o A358259 from itertools import count
%o A358259 def A358259(n):
%o A358259 b, bdict, k = 0, {0:(1,)},1<<n-1 if n > 1 else 0
%o A358259 for m in count(2):
%o A358259 if b >= k:
%o A358259 return m-1
%o A358259 if len(l := bdict[b]) > 1:
%o A358259 b = m-1-l[-2]
%o A358259 if b in bdict:
%o A358259 bdict[b] = (bdict[b][-1],m)
%o A358259 else:
%o A358259 bdict[b] = (m,)
%o A358259 else:
%o A358259 b = 0
%o A358259 bdict[0] = (bdict[0][-1],m) # _Chai Wah Wu_, Nov 06 2022
%Y A358259 Cf. A181391, A358168, A358180, A358258.
%K A358259 nonn,base
%O A358259 1,2
%A A358259 _Michael De Vlieger_, Nov 05 2022
%E A358259 a(30)-a(34) from _Chai Wah Wu_, Nov 06 2022
%E A358259 a(35) from _Martin Ehrenstein_, Nov 07 2022