A376508 Natural numbers whose iterated squaring modulo 100 eventually enters the 4-cycle 16, 56, 36, 96.

2, 4, 6, 8, 12, 14, 16, 22, 28, 34, 36, 38, 42, 44, 46, 48, 52, 54, 56, 58, 62, 64, 66, 72, 78, 84, 86, 88, 92, 94, 96, 98, 102, 104, 106, 108, 112, 114, 116, 122, 128, 134, 136, 138, 142, 144, 146, 148, 152, 154, 156, 158, 162, 164, 166, 172, 178, 184, 186

Offset

1,1

Comments

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).

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, ...

References

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).

Links

Table of n, a(n) for n=1..59.

Index entries for linear recurrences with constant coefficients, signature (1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, -1).

Example

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

Crossrefs

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

Sequence in context: A015929 A331994 A043723 * A331681 A006998 A043726

Adjacent sequences: A376505 A376506 A376507 * A376509 A376510 A376511

Keyword

nonn

Author

Martin Renner, Sep 25 2024

Status

approved