cp's OEIS Frontend

A384296 Square numbers whose iterative sums of digits are squares.

%I A384296 #29 Jul 27 2025 17:59:42
%S A384296 0,1,4,9,36,81,100,121,144,225,324,400,441,900,1521,2025,2304,2601,
%T A384296 3600,8100,10000,10201,10404,11025,12100,12321,14400,22500,32400,
%U A384296 40000,40401,44100,62001,69696,90000,101124,103041,121104,123201,149769,152100,173889,178929,199809,202500,230400,251001
%N A384296 Square numbers whose iterative sums of digits are squares.
%e A384296 10201 = 101^2. 1+0+2+0+1 = 4, 4 = 2^2.
%e A384296 178929 = 423^2. 1+7+8+9+2+9 = 36, 36 = 6^2. 3+6 = 9, 9 = 3^2.
%p A384296 filter:= proc(n) local L,i,t;
%p A384296   t:= n;
%p A384296   do
%p A384296     if not issqr(t) then return false fi;
%p A384296     if t < 10 then return true fi;
%p A384296     t:= convert(convert(t,base,10),`+`)
%p A384296   od
%p A384296 end proc:
%p A384296 select(filter, [seq(i^2,i=0..1000)]); # _Robert Israel_, May 25 2025
%t A384296 q[n_] := AllTrue[FixedPointList[DigitSum, n], IntegerQ[Sqrt[#]] &]; Select[Range[0, 500]^2, q] (* _Amiram Eldar_, May 25 2025 *)
%Y A384296 Cf. A004159, A117676, A070027.
%Y A384296 A subsequence of A053057.
%K A384296 nonn,base
%O A384296 1,3
%A A384296 _Huaineng He_, May 24 2025