A065816 Numbers k such that the alternating sum of digits of k^2 is 0.

11, 22, 33, 55, 66, 88, 99, 110, 121, 132, 165, 198, 209, 220, 231, 242, 264, 319, 330, 374, 385, 429, 451, 462, 484, 495, 506, 517, 528, 550, 561, 583, 605, 616, 649, 660, 671, 682, 715, 737, 748, 814, 836, 847, 880, 891, 902, 913, 924, 935, 957, 990

Offset: 1

Author

Robert G. Wilson v, Dec 06 2001

Keywords

• nonn
• base

Links

• Harry J. Smith, Table of n, a(n) for n = 1..1000

Crossrefs

Cf. A065796.

Programs

Mathematica

f[n_] := Block[ {d = Reverse[ IntegerDigits[ n]], k = l = 1, s = 0}, l = Length[d]; While[ k <= l, s = s - (-1)^k*d[[k]]; k++ ]; Return[s]]; Select[ Range[10^3], f[ #^2] == 0 & ]
Select[Range[1000],Total[Times@@@Partition[Riffle[IntegerDigits[#^2],{1,-1},{2,-1,2}],2]]==0&] (* Harvey P. Dale, Dec 19 2021 *)

PARI

SumAD(x)= { local(a=1, s=0); while (x>9, s+=a*(x-10*(x\10)); x\=10; a=-a); return(s + a*x) } { n=0; for (m=1, 10^9, if (SumAD(m^2) == 0, write("b065816.txt", n++, " ", m); if (n==1000, return)) ) } \\ Harry J. Smith, Oct 31 2009