allocated for Mark Anthony Larman
allocated
approved
editing
a(n) = n^4 - 2*n^3 + n^2 - 2*n + 2 for n >= 5
n=9: digits {9,7,6,2}: 9762 - 2679 (bijective base 9) = 7184 - 2016 = 5168 = "6972", the same digit multiset.
proposed
editing
nonn,base,changed
proposed
nonn,base,easy,changed
392, 890, 1752, 3122, 5168, 8082, 12080, 17402, 24312, 33098, 44072, 57570, 73952, 93602, 116928, 144362, 176360, 213402, 255992, 304658, 359952, 422450, 492752
a(n) is a fixed point of the bijective digit-sorting subtraction map applied to 4-digit numerals in base n (for n >= 5). The map sorts digits descending and ascending, subtracts, and repeats. For n >= 5, a(n) corresponds to the zeroless analogue of the Kaprekar constant sequence A099009, though the values do not match. Convergence is not universal: numerals may stabilize at a fixed point, enter a cycle, or collapse to the empty string. The fixed point is unique for 5 <= n <= 23 except n = 10, 15, and 20, where exactly two fixed points exist (a pattern proved for n == 0 (mod 5), n >= 10). Exhaustive enumeration confirms the basin structure for n <= 23; fixed-point counts are verified through n = 30. For base 9, the basin contains 6440 of 6561 initial numerals, with a maximum transient length of 7. The fixed point digits follow the pattern n-3, n, n-2, 2, derived from the invariant max - min = n - 2 with middle difference 1.
a(n) = n^4 - 2*n^3 + n^2 - 2*n + 2 for n >= 5.
editing
allocated for Mark Anthony Larman
allocated
approved