A118881 - OEIS

%I #39 Nov 19 2021 11:25:45

%S 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,

%T 49,64,81,100,121,9,16,25,36,49,64,81,100,121,144,16,25,36,49,64,81,

%U 100,121,144,169,25,36,49,64,81,100,121,144,169,196,36,49,64,81,100,121,144

%N Square of sum of decimal digits of n.

%C 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

%H N. J. A. Sloane, <a href="/A118881/b118881.txt">Table of n, a(n) for n = 0..10000</a>

%H Diophante, <a href="http://www.diophante.fr/problemes-par-themes/arithmetique-et-algebre/a1-pot-pourri/123-a1915-jongleries-nd2-avec-les-chiffres">A1915, Jongleries n°2 avec les chiffres</a> (in French).

%H Michael Penn, <a href="https://www.youtube.com/watch?v=BiItd78ihEg">squaring the sum of digits</a>, YouTube video, 2021.

%F a(n) = A007953(n)^2. [_R. J. Mathar_, Apr 22 2010]

%e From _R. J. Mathar_, Jul 08 2012: (Start)

%e Trajectories of the map x->a(x), A177148:

%e 1 ->1 ->1 ->1 ->1 ->1 ->1 ->1 ->1 ->...

%e 2 ->4 ->16 ->49 ->169 ->256 ->169 ->256 ->169 ->...

%e 3 ->9 ->81 ->81 ->81 ->81 ->81 ->81 ->81 ->...

%e 4 ->16 ->49 ->169 ->256 ->169 ->256 ->169 ->256 ->...

%e 5 ->25 ->49 ->169 ->256 ->169 ->256 ->169 ->256 ->...

%e 6 ->36 ->81 ->81 ->81 ->81 ->81 ->81 ->81 ->...

%e 7 ->49 ->169 ->256 ->169 ->256 ->169 ->256 ->169 ->...

%e 8 ->64 ->100 ->1 ->1 ->1 ->1 ->1 ->1 ->... (End)

%p read("transforms") :

%p A118881 := proc(n)

%p         digsum(n)^2 ;

%p end proc: # _R. J. Mathar_, Jul 08 2012

%t Table[Total[IntegerDigits[n]]^2,{n,0,70}] (* _Harvey P. Dale_, Jul 31 2012 *)

%o (PARI) a(n) = sumdigits(n)^2; \\ _Michel Marcus_, Mar 08 2021

%o (Python)

%o def a(n): return sum(map(int, str(n)))**2

%o print([a(n) for n in range(67)]) # _Michael S. Branicky_, Nov 19 2021

%Y Cf. A007953.

%K base,easy,nonn

%O 0,3

%A _Giovanni Teofilatto_, May 25 2006