A216997 -id:A216997 - 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 *)

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 *)

A217009 Multiples of 7 in base 8.

Original entry on oeis.org

7, 16, 25, 34, 43, 52, 61, 70, 77, 106, 115, 124, 133, 142, 151, 160, 167, 176, 205, 214, 223, 232, 241, 250, 257, 266, 275, 304, 313, 322, 331, 340, 347, 356, 365, 374, 403, 412, 421, 430, 437, 446, 455, 464, 473, 502, 511, 520, 527, 536, 545, 554, 563

Offset: 1

Jon Perry, Sep 23 2012

Digit sum is always divisible by 7.

Reinterpreting this sequence in base 10, these are numbers of the form 9n + 7 but with all numbers containing 8s and/or 9s removed. - Alonso del Arte, Sep 23 2012

			a(10) = 106 because 7 * 10 = 70, or 1 * 8^2 + 0 * 8^1 + 6 * 8^0 = 64 + 6 = 106_8.

Cf. A216994, A216995, A216996, A216997, A216998.

Cf. A008589.

k = 7;
for (i = 1; i <= 200; i++) {
x = i * k;
document.write(x.toString(k + 1) + ", ");
}

Table[BaseForm[7*n, 8], {n, 100}] (* Alonso del Arte, Sep 23 2012 *)
Select[9*Range[0, 99] + 7, DigitCount[#, 10, 8] == 0 && DigitCount[#, 10, 9] == 0 &] (* Alonso del Arte, Sep 23 2012 *)
Table[FromDigits[IntegerDigits[7*n, 8]], {n, 100}] (* T. D. Noe, Sep 24 2012 *)

a(n) = A007094(A008589(n)). -

A218292 Multiples of 10 such that the sum of their digits is also a multiple of 10.

Original entry on oeis.org

190, 280, 370, 460, 550, 640, 730, 820, 910, 1090, 1180, 1270, 1360, 1450, 1540, 1630, 1720, 1810, 1900, 2080, 2170, 2260, 2350, 2440, 2530, 2620, 2710, 2800, 2990, 3070, 3160, 3250, 3340, 3430, 3520, 3610, 3700, 3890, 3980, 4060, 4150, 4240, 4330, 4420, 4510

Offset: 1

Bruno Berselli, Oct 25 2012

			a(38) = 3890 is a multiple of 10, and 3+8+9+0=20 is also a multiple of 10.

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

Cf. multiples of k with digit sum divisible by k: A008585 (k=3), A008591 (k=9), A062753 (k=4), A179082 (k=2), A216994 (k=7), A216995 (k=11), A216997 (k=8), A218290 (k=5), A218291 (k=6).

[n: n in [10..4600 by 10] | IsZero(&+Intseq(n) mod 10)];

Select[ Range[10, 4600, 10], Mod[ Total[ IntegerDigits[#]], 10] == 0 &] (* Jean-François Alcover, Oct 26 2012 *)

a(n) = 10*A094677(n).

A218290 Multiples of 5 such that the sum of their digits is also a multiple of 5.

Original entry on oeis.org

5, 50, 55, 140, 145, 190, 195, 230, 235, 280, 285, 320, 325, 370, 375, 410, 415, 460, 465, 500, 505, 550, 555, 640, 645, 690, 695, 730, 735, 780, 785, 820, 825, 870, 875, 910, 915, 960, 965, 1040, 1045, 1090, 1095, 1130, 1135, 1180, 1185, 1220, 1225, 1270

Offset: 1

Bruno Berselli, Oct 25 2012

			145 is a multiple of 5, and its digits, 1, 4, 5, add up to 10, which is also a multiple of 5. [_Alonso del Arte_, Oct 27 2012]

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

Cf. multiples of k with digit sum divisible by k: A008585 (k = 3), A008591 (k = 9), A062753 (k = 4), A179082 (k = 2), A216994 (k = 7), A216995 (k = 11), A216997 (k = 8), A218291 (k = 6), A218292 (k = 10).

[n: n in [5..1300 by 5] | IsZero(&+Intseq(n) mod 5)];

Select[ Range[5, 1300, 5], Mod[ Total[ IntegerDigits[#]], 5] == 0 &] (* Jean-François Alcover, Oct 26 2012 *)

A218291 Multiples of 6 such that the sum of their digits is also a multiple of 6.

Original entry on oeis.org

6, 24, 42, 48, 60, 66, 84, 114, 132, 138, 150, 156, 174, 192, 198, 204, 222, 228, 240, 246, 264, 282, 288, 312, 318, 330, 336, 354, 372, 378, 390, 396, 402, 408, 420, 426, 444, 462, 468, 480, 486, 510, 516, 534, 552, 558, 570, 576, 594, 600, 606, 624, 642, 648

Offset: 1

Bruno Berselli, Oct 25 2012

			48 is a multiple of 6, and 4+8=12 is also a multiple of 6.

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

Subsequence of A179082.

Cf. multiples of k with digit sum divisible by k: A008585 (k=3), A008591 (k=9), A062753 (k=4), A179082 (k=2), A216994 (k=7), A216995 (k=11), A216997 (k=8), A218290 (k=5), A218292 (k=10).

[n: n in [6..700 by 6] | IsZero(&+Intseq(n) mod 6)];

Select[ Range[6, 700, 6], Mod[ Total[ IntegerDigits[#]], 6] == 0 &] (* Jean-François Alcover, Oct 26 2012 *)

cp's OEIS Frontend

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

Views

Author

Keywords

Comments

Examples

Links

Crossrefs

Programs

JavaScript

Mathematica

Python

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

Views

Author

Keywords

Comments

Examples

Crossrefs

Programs

JavaScript

Mathematica

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

Views

Author

Keywords

Comments

Examples

Links

Crossrefs

Programs

JavaScript

Maple

Mathematica

A216998 Digit sum of n*7 mod 7.

Views

Author

Keywords

Comments

Examples

Crossrefs

Programs

JavaScript

Mathematica

A217009 Multiples of 7 in base 8.

Views

Author

Keywords

Comments

Examples

Crossrefs

Programs

JavaScript

Mathematica

Formula

A218292 Multiples of 10 such that the sum of their digits is also a multiple of 10.

Views

Author

Keywords

Examples

Links

Crossrefs

Programs

Magma

Mathematica

Formula

A218290 Multiples of 5 such that the sum of their digits is also a multiple of 5.

Views

Author

Keywords

Examples

Links

Crossrefs

Programs

Magma

Mathematica

A218291 Multiples of 6 such that the sum of their digits is also a multiple of 6.

Views

Author