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 A101202 #40 Sep 18 2024 16:32:46
%S A101202 142857,285714,428571,571428,714285,857142,999999,1142856,1285713,
%T A101202 1428570,1571427,1714284,1857141,1999998,2142855,2285712,2428569,
%U A101202 2571426,2714283,2857140,2999997,3142854,3285711,3428568,3571425,3714282,3857139,3999996,4142853,4285710
%N A101202 Multiples of 142857.
%C A101202 This sequence is interesting because the first six terms are cyclic shifts of one another (in decimal).
%C A101202 The number 142857 is the only number such that every cyclic permutation of it is a multiple of it. This number, its double, and numbers formed from either of them by an arbitrary number of repetitions of its sequence of digits are the only ones which generate more than one multiple of themselves in the sequence of their cyclic permutations. See the Kraitchik reference. - _Martin Renner_, Mar 06 2014
%C A101202 Actually, the second claim by Kraitchik is incorrect. Indeed, there are other numbers which generate more than one multiple of themselves, for example 153846 * {3, 4} = {461538, 615384} and 230769 * {3, 4} = {692307, 923076}. - _Giovanni Resta_, Mar 11 2014
%C A101202 The digits of each term can be partitioned into two parts with the right part always consisting of 3 digits and the left part containing all the remaining digits; adding then those two numbers will yield a sum which is multiple of 999: (142+857)/999 = 1 .. (857+142)/999 = 1 (999+999)/999 = 2 (1142+856)/999 = 2 .. (1857+141)/999 = 2 (2142+855)/999 = 3 .. (2857+140)/999 = 3 (2999+997)/999 = 4 .. As a result of above operations the sequence A054896 starting with the term 8 is produced. - _Alexander R. Povolotsky_, Nov 02 2007
%C A101202 1/7 = 0.142857142857142857... - _Harvey P. Dale_, Aug 26 2014
%D A101202 Maurice Kraitchik, Mathematical Recreations, New York, Dover (2nd. ed.) 1953, p. 75-76.
%D A101202 David Wells, The Penguin Dictionary of Curious and Interesting Numbers. Penguin Books, NY, 1986, Revised edition 1987. See entry 142857 at pp. 179-183.
%H A101202 Vincenzo Librandi, <a href="/A101202/b101202.txt">Table of n, a(n) for n = 1..1000</a>
%H A101202 Tanya Khovanova, <a href="http://www.tanyakhovanova.com/RecursiveSequences/RecursiveSequences.html">Recursive Sequences</a>
%H A101202 <a href="/index/Rec#order_02">Index entries for linear recurrences with constant coefficients</a>, signature (2,-1).
%F A101202 G.f.: 142857*x/(1-x)^2. - _Alexander R. Povolotsky_, Apr 26 2008
%F A101202 a(n) = 142857*n. - _Robert Israel_, May 14 2008
%F A101202 E.g.f.: 142857*x*exp(x). - _Stefano Spezia_, Sep 18 2024
%t A101202 CoefficientList[Series[142857/(1 - x)^2, {x, 0, 40}], x] (* _Vincenzo Librandi_, Mar 13 2014 *)
%t A101202 142857*Range[30] (* _Harvey P. Dale_, Aug 26 2014 *)
%Y A101202 Cf. A054896.
%K A101202 easy,nonn
%O A101202 1,1
%A A101202 _Paul Boddington_, Dec 12 2004