A216996 Numbers n such that the digit sum of n*7 is a multiple of 7.

1, 10, 11, 19, 38, 46, 47, 56, 57, 65, 73, 74, 83, 84, 92, 100, 101, 110, 111, 119, 138, 145, 155, 163, 164, 172, 182, 190, 191, 209, 218, 228, 236, 237, 245, 255, 263, 264, 272, 282, 289, 299, 308, 316, 317, 326, 327, 335, 343, 344, 353, 354, 362, 380, 381

Offset

1,2

Comments

If n is in the sequence, so are 10*n and 10*n+1. - Robert Israel, Mar 08 2018

Links

Robert Israel, Table of n, a(n) for n = 1..10000

Example

7*19 = 133 and 1+3+3=7.

Maple

filter:= n -> convert(convert(7*n, base, 10), `+`) mod 7 = 0:
select(filter, [$1..1000]); # Robert Israel, Mar 08 2018

Mathematica

Select[Range[500], Mod[Total[IntegerDigits[7*#]], 7] == 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=7;
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+", ");
}

Crossrefs

Cf. A216994, A216995, A216997, A216998, A217009.

Sequence in context: A225079 A214790 A191221 * A165265 A329818 A329447

Adjacent sequences: A216993 A216994 A216995 * A216997 A216998 A216999

Keyword

nonn,base

Author

Jon Perry, Sep 22 2012

Status

approved