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 A327981 #16 Jun 27 2023 19:42:37
%S A327981 1,2,1,1,3,1,4,2,1,3,3,1,1,2,2,1,1,3,1,1,2,2,2,1,5,1,3,2,2,1,2,2,2,1,
%T A327981 1,1,1,1,5,1,1,1,4,2,2,1,1,6,3,2,1,4,1,1,4,1,2,1,2,1,2,8,4,1,1,1,1,2,
%U A327981 1,1,2,3,1,1,4,1,1,2,2,1,1,6,1,3,4,1,3,1,1,1,3,1,1,1,1,1,7,1,1,1,1,1,1,2,1,3,2,1,2,1,1
%N A327981 Distances between successive ones in A051023, the middle column of rule-30 1-D cellular automaton, when started from a lone 1 cell.
%C A327981 First differences of A327984, which gives indices of ones in A051023.
%H A327981 Antti Karttunen, <a href="/A327981/b327981.txt">Table of n, a(n) for n = 1..100000</a>
%F A327981 a(n) = A327984(1+n) - A327984(n).
%e A327981 The evolution of one-dimensional cellular automaton rule 30 proceeds as follows, when started from a single alive (1) cell:
%e A327981 0: (1)
%e A327981 1: 1(1)1
%e A327981 2: 11(0)01
%e A327981 3: 110(1)111
%e A327981 4: 1100(1)0001
%e A327981 5: 11011(1)10111
%e A327981 6: 110010(0)001001
%e A327981 7: 1101111(0)0111111
%e A327981 8: 11001000(1)11000001
%e A327981 9: 110111101(1)001000111
%e A327981 10: 1100100001(0)1111011001
%e A327981 11: 11011110011(0)10000101111
%e A327981 12: 110010001110(0)110011010001
%e A327981 13: 1101111011001(1)1011100110111
%e A327981 The distances between successive 1's in its central column (indicated here with parentheses) are 1-0 (as the first 1 is on row 0, and the second is on row 1), 3-1, 4-3, 5-4, 8-5, 9-8, 13-9, ..., that is, the first terms of this sequence: 1, 2, 1, 1, 3, 1, 4, ...
%t A327981 A327981list[upto_]:=Differences[Flatten[Position[CellularAutomaton[30,{{1},0},{upto,{{0}}}],1]]];A327981list[300] (* _Paolo Xausa_, Jun 27 2023 *)
%o A327981 (PARI)
%o A327981 up_to = 105;
%o A327981 A269160(n) = bitxor(n, bitor(2*n, 4*n));
%o A327981 A327981list(up_to) = { my(v=vector(up_to), s=1, n=0, on=n, k=0); while(k<up_to, n++; s = A269160(s); if((s>>n)%2, k++; v[k] = (n-on); on=n)); (v); }
%o A327981 v327981 = A327981list(up_to);
%o A327981 A327981(n) = v327981[n];
%Y A327981 Cf. A051023, A110240, A269160, A327980, A327982, A327983, A327984.
%K A327981 nonn
%O A327981 1,2
%A A327981 _Antti Karttunen_, Oct 03 2019