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

1, 49, 100, 784, 1444, 1521, 3364, 4096, 4225, 4356, 4900, 7225, 7744, 8281, 9604, 10000, 11025, 12321, 12996, 14641, 15625, 17424, 17956, 22201, 24025, 27225, 27556, 27889, 28561, 29584, 34596, 37636, 42025, 45369, 54289, 55696, 56644, 59049, 59536, 63504

Offset

1,2

Comments

This was a puzzle mentioned on The Aperiodical website.

Links

Vincenzo Librandi, Table of n, a(n) for n = 1..1000

Paul Taylor, The Aperiodical: More or Less integer sequence solution revealed (spoilers!)

Mathematica

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

Prog

(PARI) ssd(n)=n=digits(n); sum(i=1, #n, n[i]^2)
select(n->while(n>6, n=ssd(n)); n==1, vector(1000, i, i^2)) \\ Charles R Greathouse IV, Dec 17 2013

Crossrefs

Intersection of A000290 and A007770.

Sequence in context: A354342 A230653 A019547 * A067673 A250653 A045253

Adjacent sequences: A228875 A228876 A228877 * A228879 A228880 A228881

Keyword

nonn,base

Author

T. D. Noe, Oct 07 2013

Status

approved