A118881 Square of sum of decimal digits of n.

0, 1, 4, 9, 16, 25, 36, 49, 64, 81, 1, 4, 9, 16, 25, 36, 49, 64, 81, 100, 4, 9, 16, 25, 36, 49, 64, 81, 100, 121, 9, 16, 25, 36, 49, 64, 81, 100, 121, 144, 16, 25, 36, 49, 64, 81, 100, 121, 144, 169, 25, 36, 49, 64, 81, 100, 121, 144, 169, 196, 36, 49, 64, 81, 100, 121, 144

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

read("transforms") :
A118881 := proc(n)
        digsum(n)^2 ;
end proc: # R. J. Mathar, Jul 08 2012

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

Cf. A007953.

Sequence in context: A062331 A069940 A153211 * A370812 A277342 A098733

Adjacent sequences: A118878 A118879 A118880 * A118882 A118883 A118884

Keyword

base,easy,nonn

Author

Giovanni Teofilatto, May 25 2006

Status

approved