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 A300655 #7 Mar 11 2018 17:17:31 %S A300655 1,1,1,1,2,1,1,1,3,2,3,1,3,1,1,1,4,3,4,2,2,3,2,1,4,3,4,1,4,1,1,1,5,4, %T A300655 3,3,5,4,2,2,5,2,5,3,2,2,3,1,4,4,1,3,5,4,4,1,5,4,5,1,5,1,1,1,6,5,6,4, %U A300655 3,3,3,3,3,5,3,4,4,2,4,2,6,5,6,2,2,5,4 %N A300655 a(n) is the length of the longest contiguous block of ones in the binary expansion of 1/n. %C A300655 This sequence has similarities with A038374: here we consider the binary expansion of 1/n, there the binary expansion of n. %F A300655 a(2*n) = a(n). %F A300655 a(2^k + 1) = k for any k > 0. %F A300655 a(n) = 1 iff n belongs to A300630. %e A300655 The first terms, alongside the binary representation of 1/n, are: %e A300655 n a(n) bin(1/n) with repeating digits in parentheses %e A300655 -- ---- --------------------------------------------- %e A300655 1 1 1.(0) %e A300655 2 1 0.1(0) %e A300655 3 1 0.(01) %e A300655 4 1 0.01(0) %e A300655 5 2 0.(0011) %e A300655 6 1 0.0(01) %e A300655 7 1 0.(001) %e A300655 8 1 0.001(0) %e A300655 9 3 0.(000111) %e A300655 10 2 0.0(0011) %e A300655 11 3 0.(0001011101) %e A300655 12 1 0.00(01) %e A300655 13 3 0.(000100111011) %e A300655 14 1 0.0(001) %e A300655 15 1 0.(0001) %e A300655 16 1 0.0001(0) %e A300655 17 4 0.(00001111) %e A300655 18 3 0.0(000111) %e A300655 19 4 0.(000011010111100101) %e A300655 20 2 0.00(0011) %o A300655 (PARI) a(n) = my (w=1, s=Set(), f=1/max(n,2)); while (!setsearch(s,f), while (floor(f*2^(w+1))==2^(w+1)-1, w++); s=setunion(s,Set(f)); f=frac(f*2)); return (w) %Y A300655 Cf. A038374, A300630. %K A300655 nonn,base %O A300655 1,5 %A A300655 _Rémy Sigrist_, Mar 10 2018