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A228878 Happy squares: squares whose trajectory under iteration of sum of squares of digits map includes 1. 1

%I

%S 1,49,100,784,1444,1521,3364,4096,4225,4356,4900,7225,7744,8281,9604,

%T 10000,11025,12321,12996,14641,15625,17424,17956,22201,24025,27225,

%U 27556,27889,28561,29584,34596,37636,42025,45369,54289,55696,56644,59049,59536,63504

%N Happy squares: squares whose trajectory under iteration of sum of squares of digits map includes 1.

%C This was a puzzle mentioned on The Aperiodical website.

%H Vincenzo Librandi, <a href="/A228878/b228878.txt">Table of n, a(n) for n = 1..1000</a>

%H Paul Taylor, <a href="http://aperiodical.com/2013/10/more-or-less-integer-sequence-solution-revealed-spoilers/">The Aperiodical: More or Less integer sequence solution revealed (spoilers!)</a>

%t f[n_] := Total[IntegerDigits[n]^2]; Select[Range[400]^2, NestWhile[f, #, UnsameQ, All] == 1 &]

%o (PARI) ssd(n)=n=digits(n); sum(i=1, #n, n[i]^2)

%o select(n->while(n>6, n=ssd(n)); n==1, vector(1000,i,i^2)) \\ _Charles R Greathouse IV_, Dec 17 2013

%Y Intersection of A000290 and A007770.

%K nonn,base

%O 1,2

%A _T. D. Noe_, Oct 07 2013

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Last modified December 5 11:56 EST 2021. Contains 349557 sequences. (Running on oeis4.)