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 A330524 #14 Dec 18 2019 14:29:55 %S A330524 1,1,2,1,3,2,2,3,3,4,1,4,2,4,3,5,2,5,3,6,1,8,1,9,2,8,2,9,3,7,4,4,5,4, %T A330524 8,3,8,4,9,4,10,2,11,2,13,1,10,4,11,3,9,5,8,5,9,6,4,15,2,16,1,16,2,17, %U A330524 2,18,4,16,3,10,5,10,6,5,11,4,17,3,11,5,14 %N A330524 Lexicographically earliest sequence of positive terms such that for any distinct i and j, a(i) | a(j+1) <> a(j) | a(j+1) (where "|" corresponds to binary concatenation, A163621). %C A330524 This sequence is a binary variant of A318225. %C A330524 This sequence has similarities with A088177; here we combine successive terms by concatenation, there by multiplication. %C A330524 This sequence is necessarily unbounded. %C A330524 Also, the value 1 appears infinitely many times. %H A330524 Rémy Sigrist, <a href="/A330524/b330524.txt">Table of n, a(n) for n = 1..10000</a> %e A330524 The first terms, alongside their binary representation and that of the concatenation of two consecutive terms, are: %e A330524 n a(n) bin(a(n)) bin(a(n)|a(n+1)) %e A330524 -- ---- --------- ---------------- %e A330524 1 1 1 11 %e A330524 2 1 1 110 %e A330524 3 2 10 101 %e A330524 4 1 1 111 %e A330524 5 3 11 1110 %e A330524 6 2 10 1010 %e A330524 7 2 10 1011 %e A330524 8 3 11 1111 %e A330524 9 3 11 11100 %e A330524 10 4 100 1001 %e A330524 11 1 1 1100 %e A330524 12 4 100 10010 %o A330524 (PARI) s=0; v=1; for (n=1, 81, print1 (v", "); for (w=1, oo, if (!bittest(s, k=v*2^#binary(w)+w), s+=2^k; v=w; break))) %Y A330524 See A330525 for the concatenation of consecutive terms. %Y A330524 Cf. A088177, A163621, A318225. %K A330524 nonn,base %O A330524 1,3 %A A330524 _Rémy Sigrist_, Dec 17 2019