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A066564
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Numbers that when incremented by the sum of their digits produce a square.
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7
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0, 2, 8, 17, 27, 38, 72, 86, 135, 161, 179, 216, 245, 275, 315, 347, 432, 467, 521, 558, 614, 662, 720, 770, 830, 882, 944, 998, 1016, 1080, 1145, 1220, 1278, 1355, 1433, 1512, 1583, 1664, 1746, 1829, 1922, 1998, 2016, 2111, 2189, 2286, 2384, 2483, 2583
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OFFSET
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1,2
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LINKS
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EXAMPLE
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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
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MATHEMATICA
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Select[Range[0, 2600], IntegerQ[Sqrt[#+Total[IntegerDigits[#]]]]&] (* Harvey P. Dale, May 19 2012 *)
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PROG
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(PARI) digitsum(n) = local(s, d); s = 0; while(n>0, d = divrem(n, 10); n = d[1]; s = s+d[2]); s
a066564(m) = local(n); for(n = 0, m, if(issquare(n+digitsum(n)), print1(n, ", ")))
a066564(10000)
(PARI) SumD(x)= { local(s=0); while (x>9, s+=x%10; x\=10); return(s + x) }
{ 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
(PARI) isok(n) = issquare(n + sumdigits(n)); \\ Michel Marcus, Jan 15 2016
(Magma) [n: n in [0..3*10^3] | IsSquare(&+Intseq(n)+n)]; // Vincenzo Librandi, Jan 15 2016
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CROSSREFS
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KEYWORD
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base,nonn
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AUTHOR
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EXTENSIONS
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STATUS
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approved
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