A377086 Number of fixed points 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, 2, 2, 1, 1, 4, 3, 4, 2, 3, 1, 3, 5, 2, 4, 4, 2, 4, 1, 3, 3, 3, 1, 5, 2, 3, 5, 4, 4, 9, 2, 1, 1, 4, 2, 6, 4, 1, 2, 5, 3, 6, 3, 1, 2, 3, 1, 7, 2, 1, 3, 3, 1, 5, 4, 6, 5, 4, 2, 8, 3, 2, 7, 3, 1, 4, 4, 2, 3, 6, 3, 9, 2, 3, 4, 9, 3, 7, 3, 2, 6, 5, 1, 7, 3, 3, 3
Offset: 2
A377087 Number of cycles 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.
0, 1, 0, 1, 2, 1, 2, 0, 3, 2, 5, 2, 4, 1, 3, 3, 3, 2, 3, 4, 1, 5, 3, 7, 2, 3, 3, 3, 4, 4, 5, 3, 6, 12, 2, 1, 3, 2, 6, 10, 4, 8, 6, 3, 4, 2, 3, 1, 3, 4, 9, 3, 2, 2, 5, 7, 4, 8, 7, 5, 6, 6, 6, 1, 8, 7, 4, 6, 6, 2, 5, 7, 5, 5, 4, 5, 3, 4, 3, 5, 2, 4, 7, 8, 3, 7, 7
Offset: 2
Comments
If b>=2 and a>=b^3 then E(a,2,b)
Examples
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 and three cycles. Therefore a(10) = 3.
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.
Comments
Examples
Links
Crossrefs