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Multiples of 11 whose digit sum is a multiple of 11.
10

%I #27 Jul 12 2021 04:13:32

%S 209,308,407,506,605,704,803,902,2090,2299,2398,2497,2596,2695,2794,

%T 2893,2992,3080,3289,3388,3487,3586,3685,3784,3883,3982,4070,4279,

%U 4378,4477,4576,4675,4774,4873,4972,5060,5269,5368,5467,5566,5665,5764,5863,5962,6050

%N Multiples of 11 whose digit sum is a multiple of 11.

%C Nothing between 1000 and 2000.

%C Also, there are no a(n) from 10902 to 12198 (this interval contains 117 multiples of 11). [_Bruno Berselli_, Oct 26 2012]

%H Bruno Berselli, <a href="/A216995/b216995.txt">Table of n, a(n) for n = 1..1000</a>

%e 3487 = 11*317 and 3+4+8+7 = 22 = 11*2.

%t Select[11*Range[1000], Mod[Total[IntegerDigits[#]], 11] == 0 &] (* _T. D. Noe_, Sep 24 2012 *)

%o (JavaScript)

%o function sumarray(arr) {

%o t=0;

%o for (i=0;i<arr.length;i++) t+=arr[i];

%o return t;

%o }

%o k=11;

%o for(s=1;s<1000;s++) {

%o a=new Array();

%o x=(s*k).toString();

%o for (j=0;j<x.length;j++) a[j]=Number(x.charAt(j));

%o if (sumarray(a)%k==0) document.write(s*k+",");

%o }

%o (Python)

%o def sd(n): return sum(map(int, str(n)))

%o def ok(n): return n%11 == 0 and sd(n)%11 == 0

%o print(list(filter(ok, range(1, 6051)))) # _Michael S. Branicky_, Jul 11 2021

%Y Cf. A008593 (multiples of 11), A166311 (digit sum multiple of 11).

%Y Cf. A216994, A216996, A216997, A216998, A217009.

%K nonn,base

%O 1,1

%A _Jon Perry_, Sep 22 2012