A377088 Number of attractors under iteration of the map sending a positive integer to the product of its leading base-n digit and the sum of the squares of its base-n digits.

1, 5, 2, 3, 8, 6, 11, 4, 16, 14, 23, 18, 42, 7, 24, 34, 26, 58, 98, 51, 99, 88, 51, 57, 103, 72, 89, 60, 69, 35, 78, 146, 39, 90, 73, 11, 109, 113, 71, 156, 220, 93, 176, 101, 132, 172, 187, 10, 160, 95, 221, 226, 69, 55, 163, 110, 137, 287, 168, 69, 260, 194, 208

Offset

2,2

Comments

If b>=2 and a>=b^3 then E(a,2,b)<a. For each positive integer a, there is an positive integer m such that E^m(a,2,b)<b^3. (Fox et al., 2024, Lemma 4).

Links

Nathan Fox, Table of n, a(n) for n = 2..100

N. Bradley Fox et al., Elated Numbers, arXiv:2409.09863 [math.NT], 2024.

Example

In the decimal system all integers go to (1), (298), (46, 208, 136), (26, 80, 512, 150), or (33, 54, 205, 58, 445, 228, 144) under iteration of the map A376270, hence there are two fixed points, one 3-cycle, one 4-cycle, and one 7-cycle. Therefore a(10) = 1 + 1 + 3 + 4 + 7 = 16.

Crossrefs

Cf. A376270, A376272, A377086, A377087.

A193586 is the analog for happy numbers.

Sequence in context: A374957 A176319 A376913 * A261026 A378714 A160080

Adjacent sequences: A377085 A377086 A377087 * A377089 A377090 A377091

Keyword

nonn,base

Author

N. Bradley Fox, Nathan Fox, Helen Grundman, Rachel Lynn, Changningphaabi Namoijam, Mary Vanderschoot, Oct 15 2024

Status

approved