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 A376509 #8 Sep 30 2024 14:54:37 %S A376509 3,9,11,13,17,19,21,23,27,29,31,33,37,39,41,47,53,59,61,63,67,69,71, %T A376509 73,77,79,81,83,87,89,91,97,103,109,111,113,117,119,121,123,127,129, %U A376509 131,133,137,139,141,147,153,159,161,163,167,169,171,173,177,179,181 %N A376509 Natural numbers whose iterated squaring modulo 100 eventually enters the 4-cycle 21, 41, 81, 61. %C A376509 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 (cf. A376506), 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 (this sequence). %C A376509 The first-order differences of the numbers in this sequence repeat with a fixed period of length sixteen: 6, 2, 2, 4, 2, 2, 2, 4, 2, 2, 2, 4, 2, 2, 6, 6, ... %D A376509 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 A376509 <a href="/index/Rec#order_17">Index entries for linear recurrences with constant coefficients</a>, signature (1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, -1). %e A376509 3^2 = 9 -> 9^2 = 81 -> 81^2 = 61 -> 61^2 = 21 -> 21^2 = 41 -> 41^2 = 81 -> ... (mod 100) %Y A376509 Cf. A008592, A017329, A376506, A376507, A376508. %K A376509 nonn %O A376509 1,1 %A A376509 _Martin Renner_, Sep 25 2024