A353907 Numbers k such that k equals {alternating sum of digits of k} raised to the power of {number of digits of k}.

1, 2, 3, 4, 5, 6, 7, 8, 9, 31381059609, 1853020188851841

Offset

1,2

Comments

These are the only terms of this sequence.

Links

Table of n, a(n) for n=1..11.

Example

31381059609 = (9-0+6-9+5-0+1-8+3-1+3)^11.

Prog

(Python)
def A(n):
   counter = 0
   S = 0
   q = n
   while q:
      q, c = q//10, q % 10
      S += (-1)** counter * c
      counter += 1
   return S ** counter
def fixed_points_of_A():
   for i in range(1, 100):
      m = int(10 ** (1 - 1/ i)) +1
      for k in range(m, 10):
         n = k**i
         e = A(n)
         if n ==e: print(n, k, i) #prints n, the value of the alternating sum, and of the power to which is raised this number.

Crossrefs

Fixed points of A353906.

Cf. A055017 (alternating sum starting from the last digit of n).

Cf. A055642 (number of digits of n).

Sequence in context: A227549 A110370 A249517 * A363271 A031044 A367306

Adjacent sequences: A353904 A353905 A353906 * A353908 A353909 A353910

Keyword

nonn,easy,base,fini,full

Author

Malo David, May 10 2022

Status

approved