A216994 Multiples of 7 such that the digit sum is divisible by 7.

7, 70, 77, 133, 266, 322, 329, 392, 399, 455, 511, 518, 581, 588, 644, 700, 707, 770, 777, 833, 966, 1015, 1085, 1141, 1148, 1204, 1274, 1330, 1337, 1463, 1526, 1596, 1652, 1659, 1715, 1785, 1841, 1848, 1904, 1974, 2023, 2093, 2156, 2212, 2219, 2282, 2289

Offset: 1

Author

Jon Perry, Sep 22 2012

Keywords

• nonn
• base

Comments

Conjecture: Every century has a representation in the sequence.

Examples

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

Crossrefs

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

Programs

JavaScript

function sumarray(arr) {
t = 0;
for (i = 0; i < arr.length; i++) t += arr[i];
return t;
}
for(s = 7; s < 3000; s += 7) {
a = new Array();
x = s.toString();
for (j = 0; j < x.length; j++) a[j] = Number(x.charAt(j));
if (sumarray(a) % 7 == 0) document.write(s + ",");
}

Mathematica

Select[7*Range[400], Mod[Total[IntegerDigits[#]], 7] == 0 &] (* T. D. Noe, Sep 24 2012 *)