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%I #32 May 17 2023 20:45:10
%S 0,2,8,17,27,38,72,86,135,161,179,216,245,275,315,347,432,467,521,558,
%T 614,662,720,770,830,882,944,998,1016,1080,1145,1220,1278,1355,1433,
%U 1512,1583,1664,1746,1829,1922,1998,2016,2111,2189,2286,2384,2483,2583
%N Numbers that when incremented by the sum of their digits produce a square.
%H Indranil Ghosh, <a href="/A066564/b066564.txt">Table of n, a(n) for n = 1..11130</a> (terms 1..1000 from Harry J. Smith)
%e 179 is in the sequence because 179 + sum of digits of 179 = 179 + 17 = 196 which is a perfect square. - _Indranil Ghosh_, Feb 10 2017
%t Select[Range[0,2600],IntegerQ[Sqrt[#+Total[IntegerDigits[#]]]]&] (* _Harvey P. Dale_, May 19 2012 *)
%o (PARI) digitsum(n) = local(s, d); s = 0; while(n>0, d = divrem(n, 10); n = d[1]; s = s+d[2]); s
%o a066564(m) = local(n); for(n = 0, m, if(issquare(n+digitsum(n)), print1(n, ", ")))
%o a066564(10000)
%o (PARI) SumD(x)= { local(s=0); while (x>9, s+=x%10; x\=10); return(s + x) }
%o { n=0; for (m=0, 10^10, if (issquare(m + SumD(m)), write("b066564.txt", n++, " ", m); if (n==1000, return)) ) } \\ _Harry J. Smith_, Mar 04 2010
%o (PARI) isok(n) = issquare(n + sumdigits(n)); \\ _Michel Marcus_, Jan 15 2016
%o (Magma) [n: n in [0..3*10^3] | IsSquare(&+Intseq(n)+n)]; // _Vincenzo Librandi_, Jan 15 2016
%Y Cf. A062028, A066566.
%K base,nonn
%O 1,2
%A _Amarnath Murthy_, Dec 18 2001
%E More terms from _Jason Earls_, Dec 20 2001
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