A216995 Multiples of 11 whose digit sum is a multiple of 11.

209, 308, 407, 506, 605, 704, 803, 902, 2090, 2299, 2398, 2497, 2596, 2695, 2794, 2893, 2992, 3080, 3289, 3388, 3487, 3586, 3685, 3784, 3883, 3982, 4070, 4279, 4378, 4477, 4576, 4675, 4774, 4873, 4972, 5060, 5269, 5368, 5467, 5566, 5665, 5764, 5863, 5962, 6050

Offset

1,1

Comments

Nothing between 1000 and 2000.

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

Links

Bruno Berselli, Table of n, a(n) for n = 1..1000

Example

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

Mathematica

Select[11*Range[1000], Mod[Total[IntegerDigits[#]], 11] == 0 &] (* T. D. Noe, Sep 24 2012 *)

Prog

(JavaScript)
function sumarray(arr) {
t=0;
for (i=0; i<arr.length; i++) t+=arr[i];
return t;
}
k=11;
for(s=1; s<1000; s++) {
a=new Array();
x=(s*k).toString();
for (j=0; j<x.length; j++) a[j]=Number(x.charAt(j));
if (sumarray(a)%k==0) document.write(s*k+", ");
}
(Python)
def sd(n): return sum(map(int, str(n)))
def ok(n): return n%11 == 0 and sd(n)%11 == 0
print(list(filter(ok, range(1, 6051)))) # Michael S. Branicky, Jul 11 2021

Crossrefs

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

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

Sequence in context: A025326 A060979 A061880 * A283742 A083512 A168424

Adjacent sequences: A216992 A216993 A216994 * A216996 A216997 A216998

Keyword

nonn,base

Author

Jon Perry, Sep 22 2012

Status

approved