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Multiples of 7 such that the digit sum is divisible by 7.
8

%I #18 Feb 18 2013 01:00:26

%S 7,70,77,133,266,322,329,392,399,455,511,518,581,588,644,700,707,770,

%T 777,833,966,1015,1085,1141,1148,1204,1274,1330,1337,1463,1526,1596,

%U 1652,1659,1715,1785,1841,1848,1904,1974,2023,2093,2156,2212,2219,2282,2289

%N Multiples of 7 such that the digit sum is divisible by 7.

%C Conjecture: Every century has a representation in the sequence.

%e 1085 = 7*155 and 1 + 0 + 8 + 5 = 14 = 7*2.

%t Select[7*Range[400], Mod[Total[IntegerDigits[#]], 7] == 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 for(s = 7; s < 3000; s += 7) {

%o a = new Array();

%o x = s.toString();

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

%o if (sumarray(a) % 7 == 0) document.write(s + ",");

%o }

%Y Cf. A216995, A216996, A216997, A216998, A217009.

%K nonn,base

%O 1,1

%A _Jon Perry_, Sep 22 2012