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 A246143 #10 Apr 14 2021 06:29:59
%S A246143 1,3,17,18,35,45,239,341,470,1180,1230,2205,5318,45652,68042,73350,
%T A246143 119458,388804,475300,773496,836779,845397,1133816,2670010
%N A246143 Index sequence for limit-block extending A004539 (base-2 representation of sqrt(2)) with first term as initial block.
%C A246143 Suppose S = (s(0), s(1), s(2), ...) is an infinite sequence such that every finite block of consecutive terms occurs infinitely many times in S. (It is assumed that A004539 is such a sequence.) Let B = B(m,k) = (s(m), s(m+1),...s(m+k)) be such a block, where m >= 0 and k >= 0. Let m(1) be the least i > m such that (s(i), s(i+1),...,s(i+k)) = B(m,k), and put B(m(1),k+1) = (s(m(1)), s(m(1)+1),...s(m(1)+k+1)). Let m(2) be the least i > m(1) such that (s(i), s(i+1),...,s(i+k)) = B(m(1),k+1), and put B(m(2),k+2) = (s(m(2)), s(m(2)+1),...s(m(2)+k+2)). Continuing in this manner gives a sequence of blocks B'(n) = B(m(n),k+n), so that for n >= 0, B'(n+1) comes from B'(n) by suffixing a single term; thus the limit of B'(n) is defined; we call it the "limiting block extension of S with initial block B(m,k)", denoted by S^ in case the initial block is s(0).
%C A246143 The sequence (m(i)), where m(0) = 0, is the "index sequence for limit-block extending S with initial block B(m,k)", as in A246128. If the sequence S is given with offset 1, then the role played by s(0) in the above definitions is played by s(1) instead, as in the case of A246142 and A246143.
%C A246143 Limiting block extensions are analogous to limit-reverse sequences, S*, defined at A245920. The essential difference is that S^ is formed by extending each new block one term to the right, whereas S* is formed by extending each new block one term to the left (and then reversing).
%e A246143 S = A004539, with B = (s(1)); that is, (m,k) = (1,0)
%e A246143 S = (1, 0, 1, 1, 0, 1, 0, 1, 0, 0, 0, 0, 0, 1, 0, ...)
%e A246143 B'(0) = (1)
%e A246143 B'(1) = (1,1)
%e A246143 B'(2) = (1,1,1)
%e A246143 B'(3) = (1,1,1,0)
%e A246143 B'(4) = (1,1,1,0,0)
%e A246143 B'(5) = (1,1,1,0,0,1)
%e A246143 S^ = (1,1,1,0,0,1,1,0,1,0,0,1,1,0,...),
%e A246143 with index sequence (1,3,17,18,35,45,239,341,...)
%t A246143 seqPosition1[list_, seqtofind_] := If[Length[#] > Length[list], {}, Last[Last[Position[Partition[list, Length[#], 1], Flatten[{___, #, ___}], 1, 1]]]] &[seqtofind]; s = RealDigits[Sqrt[2], 2, 10000000][[1]]; Take[s, 60]
%t A246143 t = {{1}}; p[0] = seqPosition1[s, Last[t]]; s = Drop[s, p[0]]; Off[Last::nolast]; n = 1; While[(p[n] = seqPosition1[s, Last[t]]) > 0, (AppendTo[t, Take[s, {#, # + Length[Last[t]]}]]; s = Drop[s, #]) &[p[n]]; n++]; On[Last::nolast]; Last[t] (*A246142*)
%t A246143 Accumulate[Table[p[k], {k, 0, n - 1}]] (*A246143*)
%Y A246143 Cf. A246142, A246127, A246144, A246146, A004539.
%K A246143 nonn,base,more
%O A246143 1,2
%A A246143 _Clark Kimberling_ and _Peter J. C. Moses_, Aug 17 2014