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
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
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, one 3-cycle, one 4-cycle, and one 7-cycle. Therefore a(10) = 1 + 1 + 3 + 4 + 7 = 16.
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