cp's OEIS Frontend

This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.

Showing 1-5 of 5 results.

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

Original entry on oeis.org

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

Views

Author

Jon Perry, Sep 22 2012

Keywords

Comments

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]

Examples

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

Links

Crossrefs

Cf. A008593 (multiples of 11), A166311 (digit sum multiple of 11).
Cf. A216994, A216996, A216997, A216998, A217009.

Programs

  • JavaScript
    function sumarray(arr) {
t=0;
for (i=0;i
  • Mathematica
    Select[11*Range[1000], Mod[Total[IntegerDigits[#]], 11] == 0 &] (* T. D. Noe, Sep 24 2012 *)
  • Python
    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

Views

Author

Jon Perry, Sep 22 2012

Keywords

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 *)

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

Views

Author

Jon Perry, Sep 22 2012

Keywords

Comments

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

Examples

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

Crossrefs

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

Programs

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

Views

Author

Jon Perry, Sep 22 2012

Keywords

Comments

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

Examples

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

Links

Crossrefs

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

Programs

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

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

Views

Author

Jon Perry, Sep 23 2012

Keywords

Comments

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

Examples

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

Crossrefs

Cf. A216994, A216995, A216996, A216997, A216998.
Cf. A008589.

Programs

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

Formula

a(n) = A007094(A008589(n)). -
Showing 1-5 of 5 results.

Started in 1964 by Neil J. A. Sloane | Maintained by The OEIS Foundation Inc.

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