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 A136042 #20 Jul 28 2025 10:54:06
%S A136042 5,4,1,2,3,1,1,1,2,1,1,3,2,1,5,4,1,2,3,1,1,1,2,1,1,3,2,1,5,4,1,2,3,1,
%T A136042 1,1,2,1,1,3,2,1,5,4,1,2,3,1,1,1,2,1,1,3,2,1,5,4,1,2,3,1,1,1,2,1,1,3,
%U A136042 2,1,5,4,1,2,3,1,1,1,2,1,1,3,2,1,5,4,1,2,3,1,1,1,2,1,1,3,2,1,5,4,1,2,3,1,1
%N A136042 Base-2 MR-expansion of 1/29.
%C A136042 The base-m MR-expansion of a positive real number x, denoted by MR(x,m), is the integer sequence {s(1),s(2),s(3),...}, where s(i) is the smallest exponent d such that (m^d)x(i)>1 and where x(i+1)=(m^d)x(i)-1, with the initialization x(1)=x. The base-2 MR-expansion of 1/29 is periodic with period length 14. Further computational results (see A136043) suggest that if p is a prime with 2 as a primitive root, then the base-2 MR-expansion of 1/p is periodic with period (p-1)/2. This has been confirmed for primes up to 2000. The base-2 MR-expansion of e=2.71828... is given in A136044.
%H A136042 <a href="/index/Rec#order_14">Index entries for linear recurrences with constant coefficients</a>, signature (0,0,0,0,0,0,0,0,0,0,0,0,0,1).
%e A136042 The MR-expansion of 1/5 using m=2 is {3,1,3,1,3,1,3,1,...}, because 1/5->2/5->4/5->8/5->3/5->6/5->1/5->... indicating that MR(1/5,2) begins {3,1,...} and has period length 2.
%Y A136042 Cf. A136043, A136044, A158379.
%K A136042 nonn,easy
%O A136042 1,1
%A A136042 _John W. Layman_, Dec 12 2007