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 A092539 #14 Feb 16 2025 08:32:52 %S A092539 1,3,6,13,27,55,110,220,441,883,1766,3532,7064,14129,28258,56517, %T A092539 113035,226070,452140,904281,1808562,3617124,7234249,14468499, %U A092539 28936999,57873998,115747997,231495994,462991989,925983979,1851967959,3703935918 %N A092539 Binary representation of a(n) equals first n+1 terms of A051023. %C A092539 a(n+1) = 2*a(n) + d, where d = 0/1 with no obvious rule. The sequence is a digit representation of the central column of cellular automaton Rule 30, A051023. Primes in the sequence, A092540. %H A092539 Reinhard Zumkeller, <a href="/A092539/b092539.txt">Table of n, a(n) for n = 0..1000</a> %H A092539 Eric Weisstein's World of Mathematics, <a href="https://mathworld.wolfram.com/Rule30.html">Rule 30</a>. %F A092539 a(n+1) = 2*a(n) + A051023(n+1). - _Reinhard Zumkeller_, Jun 08 2013 %e A092539 a(6) = 55_10 = 110111_2 %t A092539 a(n_) := FromDigits[Take[A051023, n], 2] %o A092539 (Haskell) %o A092539 a092539 n = a092539_list !! n %o A092539 a092539_list = scanl1 (\v d -> 2 * v + d) $ map toInteger a051023_list %o A092539 -- _Reinhard Zumkeller_, Jun 08 2013 %Y A092539 Cf. A051023, A092540. %K A092539 easy,nonn %O A092539 0,2 %A A092539 _Zak Seidov_, Feb 27 2004 %E A092539 Offset corrected and definition adjusted by _Reinhard Zumkeller_, Jun 08 2013