OFFSET
0,3
COMMENTS
a(k) = k iff k = 0, 1, 81; also, the only solution to the double equation a(k) = m and a(m) = k with k < m is (169, 256) (proof in Diophante link, 2ème jonglerie). - Bernard Schott, Mar 08 2021
LINKS
N. J. A. Sloane, Table of n, a(n) for n = 0..10000
Diophante, A1915, Jongleries n°2 avec les chiffres (in French).
Michael Penn, squaring the sum of digits, YouTube video, 2021.
FORMULA
a(n) = A007953(n)^2. [R. J. Mathar, Apr 22 2010]
EXAMPLE
From R. J. Mathar, Jul 08 2012: (Start)
Trajectories of the map x->a(x), A177148:
1 ->1 ->1 ->1 ->1 ->1 ->1 ->1 ->1 ->...
2 ->4 ->16 ->49 ->169 ->256 ->169 ->256 ->169 ->...
3 ->9 ->81 ->81 ->81 ->81 ->81 ->81 ->81 ->...
4 ->16 ->49 ->169 ->256 ->169 ->256 ->169 ->256 ->...
5 ->25 ->49 ->169 ->256 ->169 ->256 ->169 ->256 ->...
6 ->36 ->81 ->81 ->81 ->81 ->81 ->81 ->81 ->...
7 ->49 ->169 ->256 ->169 ->256 ->169 ->256 ->169 ->...
8 ->64 ->100 ->1 ->1 ->1 ->1 ->1 ->1 ->... (End)
MAPLE
MATHEMATICA
Table[Total[IntegerDigits[n]]^2, {n, 0, 70}] (* Harvey P. Dale, Jul 31 2012 *)
PROG
(PARI) a(n) = sumdigits(n)^2; \\ Michel Marcus, Mar 08 2021
(Python)
def a(n): return sum(map(int, str(n)))**2
print([a(n) for n in range(67)]) # Michael S. Branicky, Nov 19 2021
CROSSREFS
KEYWORD
base,easy,nonn
AUTHOR
Giovanni Teofilatto, May 25 2006
STATUS
approved