A376508 - OEIS

%I #9 Sep 30 2024 14:53:39

%S 2,4,6,8,12,14,16,22,28,34,36,38,42,44,46,48,52,54,56,58,62,64,66,72,

%T 78,84,86,88,92,94,96,98,102,104,106,108,112,114,116,122,128,134,136,

%U 138,142,144,146,148,152,154,156,158,162,164,166,172,178,184,186

%N Natural numbers whose iterated squaring modulo 100 eventually enters the 4-cycle 16, 56, 36, 96.

%C 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 (this sequence) or 21, 41, 81, 61 (cf. A376509).

%C The first-order differences of the numbers in this sequence repeat with a fixed period of length sixteen: 2, 2, 2, 4, 2, 2, 6, 6, 6, 2, 2, 4, 2, 2, 2, 4, ...

%D 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 <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 2^2 = 4 -> 4^2 = 16 -> 16^2 = 56 -> 56^2 = 36 -> 36^2 = 96, 96^2 = 16 -> ... (mod 100).

%Y Cf. A008592, A017329, A376506, A376507, A376509.

%K nonn

%O 1,1

%A _Martin Renner_, Sep 25 2024