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 A217592 #15 Dec 24 2012 02:35:54
%S A217592 0,105263157894736842,210526315789473684,315789473684210526,
%T A217592 421052631578947368,526315789473684210,631578947368421052,
%U A217592 736842105263157894,842105263157894736,947368421052631578,105263157894736842105263157894736842,210526315789473684210526315789473684
%N A217592 Integers that are cut in half by cycling all the decimal digits one place to the left.
%C A217592 A rotation of the decimal digits to the left puts the leading digit in the rightmost position (123456 becomes 234561). The (even) integers that are cut in half by this operation form 10 families; a singleton {a(0)=0} and 9 infinite families, each consisting of any number of repetitions of an 18-digit pattern.
%C A217592 Each of those families corresponds to a single decadic solution of the equation x=2(10x+d) where d is a digit from 0 to 9 (namely x=-2d/19 which is a periodic decadic).
%C A217592 This sequence is strongly related to A146088:
%C A217592 A146088(8k+1) = a(9k+2)/2 = a(9k+1)
%C A217592 A146088(8k+2) = a(9k+3)/2
%C A217592 A146088(8k+3) = a(9k+4)/2 = a(9k+2)
%C A217592 A146088(8k+4) = a(9k+5)/2
%C A217592 A146088(8k+5) = a(9k+6)/2 = a(9k+3)
%C A217592 A146088(8k+6) = a(9k+7)/2
%C A217592 A146088(8k+7) = a(9k+8)/2 = a(9k+4)
%C A217592 A146088(8k+8) = a(9k+9)/2
%C A217592 Note that a(9k+1)/2 is not part of A146088, because rotating one place to the left a decimal expansion starting with 105263157894736842 yields a discarded zero leading digit which is not retrieved by rotating the digits to the right (right-rotation would double the pattern 052631578947368421 but not the number 52631578947368421).
%C A217592 Lists normally have offset 1, but there is a good reason to make an exception in this case. - _N. J. A. Sloane_, Dec 24 2012
%H A217592 G. P. Michon, <a href="http://www.numericana.com/answer/p-adic.htm#snroy2">Numbers cut in half by rotating digits left</a> (2006).
%F A217592 a(j)=j*105263157894736842 for j = 0 to 9
%F A217592 a(n+9)=10^18*a(n) + a(n) mod 10^18 for n>0
%F A217592 a(9k-9+j) = j*a(1)*(10^18k-1)/(10^18-1) for j=1..9 and k>0
%F A217592 e.g., a(1000) = a(9*112-9+1) = a(1)*(10^2016-1)/(10^18-1)
%e A217592 a(0) = 0 because rotating a lone zero gives 0 = 0/2.
%e A217592 a(1) = 105263157894736842 because its half equals 052631578947368421 (discarding leading 0).
%e A217592 a(3) = 315789473684210526 since a(3)/2 = 157894736842105263.
%Y A217592 A146088(8k+i)=a(9k+i+1)/2 for i=1..8 and any k.
%K A217592 base,nonn,easy
%O A217592 0,2
%A A217592 _Gerard P. Michon_, Oct 28 2012