A319839 Smallest fixed points (>0) of the base-2*n Kaprekar map.

9, 30, 105, 21, 495, 858, 65, 2040, 2907, 133, 5313, 6900, 225, 10962, 13485, 341, 19635, 23310, 481, 31980, 37023, 645, 48645, 55272, 833, 70278, 78705, 1045, 97527, 107970, 1281, 131040, 143715, 1541, 171465, 186588, 1825, 219450, 237237, 2133, 275643, 296310, 2465

Offset: 1

Author

Seiichi Manyama, Sep 29 2018

Keywords

• nonn
• base
• look

Links

• Seiichi Manyama, Table of n, a(n) for n = 1..100
• Index entries for the Kaprekar map

Crossrefs

Cf. A099009, A163205, A165016, A165055, A165094, A319798.

Programs

Ruby

def f(k, n)
  ary = []
  while n > 0
    ary << n % k
    n /= k
  end
  ary
end
def g(k, ary)
  (0..ary.size - 1).inject(0){|s, i| s + ary[i] * k ** i}
end
def A319798(n)
  i = 1
  ary = [1]
  while g(n, ary) - g(n, ary.reverse) != i
    i += 1
    ary = f(n, i).sort
  end
  i
end
def A319839(n)
  (1..n).map{|i| A319798(2 * i)}
end
p A319839(20)

Formula

a(n) = A319798(2*n).