A217009 -id:A217009 - cp's OEIS frontend

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

Jon Perry, Sep 22 2012

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]

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

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

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

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

function sumarray(arr) {
t=0;
for (i=0;i

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

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

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

Original entry on oeis.org

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

Jon Perry, Sep 22 2012

Conjecture: Every century has a representation in the sequence.

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

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

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 + ",");
}

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

A216997 Multiples of 8 that have a digit sum which is a multiple of 8.

Original entry on oeis.org

8, 80, 88, 152, 224, 376, 440, 448, 512, 592, 664, 736, 800, 808, 880, 888, 952, 1016, 1096, 1160, 1168, 1232, 1304, 1384, 1456, 1520, 1528, 1672, 1744, 1816, 1896, 1960, 1968, 2024, 2176, 2240, 2248, 2312, 2392, 2464, 2536, 2600, 2608, 2680, 2688, 2752, 2824

Offset: 1

Jon Perry, Sep 22 2012

Between a(5) and a(6) there are 151 terms that does not satisfy the property. [Bruno Berselli, Oct 26 2012]

			376 = 8*47 and 3+7+6 = 16 = 8*2.

Cf. A216994, A216995, A216996, A216998, A217009.

function sumarray(arr) {
t=0;
for (i=0;i

Select[8*Range[400], Mod[Total[IntegerDigits[#]], 8] == 0 &] (* T. D. Noe, Sep 24 2012 *)

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

Original entry on oeis.org

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

Jon Perry, Sep 22 2012

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

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

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

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

function sumarray(arr) {
t=0;
for (i=0;i

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

Select[Range[500], Mod[Total[IntegerDigits[7*#]], 7] == 0 &] (* T. D. Noe, Sep 24 2012 *)

A216998 Digit sum of n*7 mod 7.

Original entry on oeis.org

0, 5, 3, 3, 1, 6, 6, 4, 2, 0, 0, 5, 3, 3, 6, 4, 4, 2, 0, 5, 5, 3, 1, 1, 6, 4, 4, 2, 5, 3, 3, 1, 6, 6, 4, 2, 2, 0, 5, 3, 3, 1, 4, 4, 2, 0, 0, 5, 3, 1, 1, 6, 4, 4, 2, 0, 0, 3, 1, 6, 6, 4, 2, 2, 0, 5, 5, 3, 1, 6, 6, 2, 0, 0, 5, 3, 3, 1, 6, 4, 4, 2, 0, 0, 5, 1, 1, 6

Offset: 1

Jon Perry, Sep 22 2012

Zeros correspond to A216994.

			a(8) corresponds to the digit sum of 56, which is 11, mod 7, so a(8)=4.

Cf. A216994, A216995, A216996, A216997, A217009.

function sumarray(arr) {
t=0;
for (i=0;i

Table[Mod[Total[IntegerDigits[7*n]], 7], {n, 100}] (* T. D. Noe, Sep 24 2012 *)

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

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

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A216997 Multiples of 8 that have a digit sum which is a multiple of 8.

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

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A216998 Digit sum of n*7 mod 7.

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