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 A376506 #9 Sep 30 2024 12:58:58 %S A376506 1,7,43,49,51,57,93,99,101,107,143,149,151,157,193,199,201,207,243, %T A376506 249,251,257,293,299,301,307,343,349,351,357,393,399,401,407,443,449, %U A376506 451,457,493,499,501,507,543,549,551,557,593,599,601,607,643,649,651,657 %N A376506 Natural numbers whose iterated squaring modulo 100 eventually settles at the attractor 1. %C A376506 The natural numbers decompose into six categories under the operation of repeated squaring modulo 100, four of which consist of numbers that eventually settle at the attractors 0 (cf. A008592), 1 (this sequence), 25 (cf. A017329), or 76 (cf. A376507), and two of which eventually enter one of the 4-cycles 16, 56, 36, 96 (cf. A376508) or 21, 41, 81, 61 (cf. A376509). %C A376506 The first-order differences of the numbers in this sequence repeat with a fixed period of length four: 6, 36, 6, 2, ... %D A376506 Alexander K. Dewdney, Computer-Kurzweil. Mit einem Computer-Mikroskop untersuchen wir ein Objekt von faszinierender Struktur in der Ebene der komplexen Zahlen. In: Spektrum der Wissenschaft, Oct 1985, p. 8-14, here p. 11-13 (Iterations on a finite set), 14 (Iteration diagram). %H A376506 <a href="/index/Rec#order_05">Index entries for linear recurrences with constant coefficients</a>, signature (1,0,0,1,-1). %F A376506 G.f.: x*(1 + 6*x + 36*x^2 + 6*x^3 + x^4)/((1 - x)^2*(1 + x + x^2 + x^3)). - _Stefano Spezia_, Sep 26 2024 %e A376506 7^2 = 49 -> 49^2 = 1 -> 1^2 = 1 -> ... (mod 100). %Y A376506 Cf. A008592, A017329, A376507, A376508, A376509. %K A376506 nonn,easy %O A376506 1,2 %A A376506 _Martin Renner_, Sep 25 2024