A279769 -id:A279769 - cp's OEIS frontend

A235228 Numbers whose sum of digits is 18.

99, 189, 198, 279, 288, 297, 369, 378, 387, 396, 459, 468, 477, 486, 495, 549, 558, 567, 576, 585, 594, 639, 648, 657, 666, 675, 684, 693, 729, 738, 747, 756, 765, 774, 783, 792, 819, 828, 837, 846, 855, 864, 873, 882, 891, 909, 918, 927, 936, 945, 954, 963

Offset: 1

Vincenzo Librandi, Jan 05 2014

A007953(a(n)) = 18; number of repdigits = #{99,666,333333,222222222,1^18} = A242627(18) = 5. - Reinhard Zumkeller, Jul 17 2014

Vincenzo Librandi, Table of n, a(n) for n = 1..1000

Cf. A052217 - A052224, A061423, A143164, A166311, A166370, A166459.
Cf. A011557 (1), A052216 (2), A052217 (3), A052218 (4), A052219 (5), A052220 (6), A052221 (7), A052222 (8), A052223 (9), A052224 (10), A166311 (11), A235151 (12), A143164 (13), A235225(14), A235226 (15), A235227 (16), A166370 (17), A166459 (19), A235229 (20).
Cf. A242614, A242627.

a235228 n = a235228_list !! (n-1)
a235228_list = filter ((== 18) . a007953) [0..]
-- Reinhard Zumkeller, Jul 17 2014

[n: n in [1..1000] | &+Intseq(n) eq 18];

Select[Range[1000], Total[IntegerDigits[#]] == 18 &]

a(n) = 9*A279769(n). - M. F. Hasler, Dec 23 2016

A279777 Numbers k such that the sum of digits of 9k is 27.

Original entry on oeis.org

111, 211, 221, 222, 311, 321, 322, 331, 332, 333, 411, 421, 422, 431, 432, 433, 441, 442, 443, 444, 511, 521, 522, 531, 532, 533, 541, 542, 543, 544, 551, 552, 553, 554, 555, 611, 621, 622, 631, 632, 633, 641, 642, 643, 644, 651, 652, 653, 654, 655, 661

Offset: 1

M. F. Hasler, Dec 23 2016

The digital sum of 9k is always a multiple of 9. For most numbers below 100 it is actually equal to 9. Numbers such that the digital sum of 9k is 18 are listed in A279769. Only every third term of the present sequence is divisible by 3.

The sequence of record gaps [and upper end of the gap] is: 100 [a(2) = 211], 101 [a(221) = 1211], 111 [a(4841) = 11211], 111 [a(10121) = 22311], 111 [a(15752) = 33411], ..., 111 [a(45133) = 88911], 111 [a(50413) = 100011], 211 [a(55253) = 111211], 311 [a(110000) = 222311], ..., 911 [a(380557) = 888911], 1011 [a(411049) = 1000011], 1211 [a(436976) = 1111211], 2311 [a(840281) = 2222311], ..., 8911 [a(2451241) = 8888911], ...

Cf. A008591, A084854, A003991, A004247, A279769 (sumdigits(9n) = 18).
Digital sum of m*n equals m: A088404 = A069537/2, A088405 = A052217/3, A088406 = A063997/4, A088407 = A069540/5, A088408 = A062768/6, A088409 = A063416/7, A088410 = A069543/8.
Numbers with given digital sum: A011557 (1), A052216 (2), A052217 (3), A052218 (4), A052219 (5), A052220 (6), A052221 (7), A052222 (8), A052223 (9), A052224 (10), A166311 (11), A235151 (12), A143164 (13), A235225 (14), A235226 (15), A235227 (16), A166370 (17), A235228 (18), A166459 (19), A235229 (20).
Cf. A007953 (digital sum), A005349 (Niven or Harshad numbers), A245062 (arranged in rows by digit sums).
Cf. A082259.

Select[Range@ 661, Total@ IntegerDigits[9 #] == 27 &] (* Michael De Vlieger, Dec 23 2016 *)

PARI
```
is(n)=sumdigits(9*n)==27
```

A279768 Numbers n such that the sum of digits of 8n equals 16.

Original entry on oeis.org

11, 47, 56, 74, 83, 92, 101, 110, 119, 137, 146, 173, 182, 191, 209, 218, 227, 245, 272, 281, 299, 308, 317, 326, 335, 344, 353, 398, 407, 416, 434, 443, 452, 470, 479, 488, 506, 524, 533, 542, 551, 560, 569, 578, 605, 614, 632, 641, 659, 668, 677, 695

Offset: 1

M. F. Hasler, Dec 23 2016

Inspired by A088410 = A069543/8 and A279769 (the analog for 9).

Cf. A007953 (digital sum), A279772 (sumdigits(2n) = 4), A279773 (sumdigits(3n) = 6), A279774 (sumdigits(4n) = 8), A279775 (sumdigits(5n) = 10), A279776 (sumdigits(6n) = 12), A279770 (sumdigits(7n) = 14), A279768 (sumdigits(8n) = 16), A279769 (sumdigits(9n) = 18), A279777 (sumdigits(9n) = 27).
Digital sum of m*n equals m: A088404 = A069537/2, A088405 = A052217/3, A088406 = A063997/4, A088407 = A069540/5, A088408 = A062768/6, A088409 = A063416/7, A088410 = A069543/8.
Cf. A005349 (Niven or Harshad numbers), A245062 (arranged in rows by digit sums).
Numbers with given digital sum: A011557 (1), A052216 (2), A052217 (3), A052218 (4), A052219 (5), A052220 (6), A052221 (7), A052222 (8), A052223 (9), A052224 (10), A166311 (11), A235151 (12), A143164 (13), A235225 (14), A235226 (15), A235227 (16), A166370 (17), A235228 (18), A166459 (19), A235229 (20).

Select[Range@ 700, Total@ IntegerDigits[8 #] == 16 &] (* Michael De Vlieger, Dec 23 2016 *)

PARI
```
is(n)=sumdigits(8*n)==16
```

A279775 Numbers k such that the sum of digits of 5k equals 10.

Original entry on oeis.org

11, 29, 38, 47, 56, 65, 74, 83, 92, 101, 110, 128, 146, 164, 182, 209, 218, 227, 236, 245, 254, 263, 272, 281, 290, 308, 326, 344, 362, 380, 407, 416, 425, 434, 443, 452, 461, 470, 488, 506, 524, 542, 560, 605, 614, 623, 632, 641, 650, 668, 686, 704, 722, 740, 803, 812, 821, 830, 848, 866, 884, 902, 920

Offset: 1

M. F. Hasler, Dec 23 2016

Inspired by A088407 = A069540/5 and A279769 (the analog for 9).

Michael S. Branicky, Table of n, a(n) for n = 1..10000

Cf. A007953 (digital sum), A279772 (sumdigits(2n) = 4), A279773 (sumdigits(3n) = 6), A279774 (sumdigits(4n) = 8), A279776 (sumdigits(6n) = 12), A279770 (sumdigits(7n) = 14), A279768 (sumdigits(8n) = 16), A279769 (sumdigits(9n) = 18), A279777 (sumdigits(9n) = 27).
Digital sum of m*n equals m: A088404 = A069537/2, A088405 = A052217/3, A088406 = A063997/4, A088407 = A069540/5, A088408 = A062768/6, A088409 = A063416/7, A088410 = A069543/8.
Cf. A005349 (Niven or Harshad numbers), A245062 (arranged in rows by digit sums).
Numbers with given digital sum: A011557 (1), A052216 (2), A052217 (3), A052218 (4), A052219 (5), A052220 (6), A052221 (7), A052222 (8), A052223 (9), A052224 (10), A166311 (11), A235151 (12), A143164 (13), A235225 (14), A235226 (15), A235227 (16), A166370 (17), A235228 (18), A166459 (19), A235229 (20).

Select[Range@ 920, Total@ IntegerDigits[5 #] == 10 &] (* Michael De Vlieger, Dec 23 2016 *)

select( is(n)=sumdigits(5*n)==10, [0..999])

def ok(n): return sum(map(int, str(5*n))) == 10
print([k for k in range(921) if ok(k)]) # Michael S. Branicky, Nov 29 2021

A279770 Numbers n such that the sum of digits of 7n equals 14.

Original entry on oeis.org

11, 38, 47, 56, 65, 74, 83, 92, 101, 110, 119, 155, 164, 182, 191, 209, 218, 236, 245, 263, 272, 299, 308, 317, 326, 335, 344, 353, 362, 380, 389, 416, 434, 452, 461, 470, 479, 488, 506, 515, 533, 560, 578, 587, 596, 605, 623, 632, 650, 659, 686, 722, 731

Offset: 1

M. F. Hasler, Dec 23 2016

Inspired by A088409 = A063416/7 and A279769 (the analog for 9).

Cf. A007953 (digital sum), A279772 (sumdigits(2n) = 4), A279773 (sumdigits(3n) = 6), A279774 (sumdigits(4n) = 8), A279775 (sumdigits(5n) = 10), A279776 (sumdigits(6n) = 12), A279768 (sumdigits(8n) = 16), A279769 (sumdigits(9n) = 18), A279777 (sumdigits(9n) = 27).
Digital sum of m*n equals m: A088404 = A069537/2, A088405 = A052217/3, A088406 = A063997/4, A088407 = A069540/5, A088408 = A062768/6, A088409 = A063416/7, A088410 = A069543/8.
Cf. A005349 (Niven or Harshad numbers), A245062 (arranged in rows by digit sums).
Numbers with given digital sum: A011557 (1), A052216 (2), A052217 (3), A052218 (4), A052219 (5), A052220 (6), A052221 (7), A052222 (8), A052223 (9), A052224 (10), A166311 (11), A235151 (12), A143164 (13), A235225 (14), A235226 (15), A235227 (16), A166370 (17), A235228 (18), A166459 (19), A235229 (20).

Select[Range@ 731, Total@ IntegerDigits[7 #] == 14 &] (* Michael De Vlieger, Dec 23 2016 *)

PARI
```
is(n)=sumdigits(7*n)==14
```

A279772 Numbers n such that the sum of digits of 2n equals 4.

Original entry on oeis.org

2, 11, 20, 56, 65, 101, 110, 155, 200, 506, 515, 551, 560, 605, 650, 1001, 1010, 1055, 1100, 1505, 1550, 2000, 5006, 5015, 5051, 5060, 5105, 5150, 5501, 5510, 5555, 5600, 6005, 6050, 6500, 10001, 10010, 10055, 10100, 10505, 10550, 11000, 15005, 15050, 15500

Offset: 1

M. F. Hasler, Dec 23 2016

Inspired by A088404 = A069537/2 and A279769 (the analog for 9).

Cf. A007953 (digital sum), A052216 (sumdigits(n) = 2), A279773 (sumdigits(3n) = 6), A279774 (sumdigits(4n) = 8), A279775 (sumdigits(5n) = 10), A279776 (sumdigits(6n) = 12), A279770 (sumdigits(7n) = 14), A279768 (sumdigits(8n) = 16), A279769 (sumdigits(9n) = 18), A279777 (sumdigits(9n) = 27).
Digital sum of m*n equals m: A088404 = A069537/2, A088405 = A052217/3, A088406 = A063997/4, A088407 = A069540/5, A088408 = A062768/6, A088409 = A063416/7, A088410 = A069543/8.
Cf. A005349 (Niven or Harshad numbers), A245062 (arranged in rows by digit sums).
Numbers with given digital sum: A011557 (1), A052216 (2), A052217 (3), A052218 (4), A052219 (5), A052220 (6), A052221 (7), A052222 (8), A052223 (9), A052224 (10), A166311 (11), A235151 (12), A143164 (13), A235225 (14), A235226 (15), A235227 (16), A166370 (17), A235228 (18), A166459 (19), A235229 (20).

Select[Range@ 15500, Total@ IntegerDigits[2 #] == 4 &] (* Michael De Vlieger, Dec 23 2016 *)

select( is(n)=sumdigits(2*n)==4, [1..9999])

A279773 Numbers n such that the sum of digits of 3n equals 6.

Original entry on oeis.org

2, 5, 8, 11, 14, 17, 20, 35, 38, 41, 44, 47, 50, 68, 71, 74, 77, 80, 101, 104, 107, 110, 134, 137, 140, 167, 170, 200, 335, 338, 341, 344, 347, 350, 368, 371, 374, 377, 380, 401, 404, 407, 410, 434, 437, 440, 467, 470, 500, 668, 671, 674, 677, 680, 701

Offset: 1

M. F. Hasler, Dec 23 2016

Inspired by A088405 = A052217/3 and A279769 (the analog for 9).

Cf. A007953 (digital sum), A279772 (sumdigits(2n) = 4), A279774 (sumdigits(4n) = 8), A279775 (sumdigits(5n) = 10), A279776 (sumdigits(6n) = 12), A279770 (sumdigits(7n) = 14), A279768 (sumdigits(8n) = 16), A279769 (sumdigits(9n) = 18), A279777 (sumdigits(9n) = 27).
Digital sum of m*n equals m: A088404 = A069537/2, A088405 = A052217/3, A088406 = A063997/4, A088407 = A069540/5, A088408 = A062768/6, A088409 = A063416/7, A088410 = A069543/8.
Cf. A005349 (Niven or Harshad numbers), A245062 (arranged in rows by digit sums).
Numbers with given digital sum: A011557 (1), A052216 (2), A052217 (3), A052218 (4), A052219 (5), A052220 (6), A052221 (7), A052222 (8), A052223 (9), A052224 (10), A166311 (11), A235151 (12), A143164 (13), A235225 (14), A235226 (15), A235227 (16), A166370 (17), A235228 (18), A166459 (19), A235229 (20).

Select[Range@ 720, Total@ IntegerDigits[3 #] == 6 &] (* Michael De Vlieger, Dec 23 2016 *)

select( is(n)=sumdigits(3*n)==6, [1..999])

A279774 Numbers n such that the sum of digits of 4n equals 8.

Original entry on oeis.org

2, 11, 20, 29, 38, 56, 65, 83, 101, 110, 128, 155, 200, 254, 263, 281, 290, 308, 326, 335, 353, 380, 425, 506, 515, 533, 551, 560, 578, 605, 650, 758, 776, 785, 803, 830, 875, 1001, 1010, 1028, 1055, 1100, 1253, 1280, 1325, 1505, 1550, 1775

Offset: 1

M. F. Hasler, Dec 23 2016

Inspired by A088406 = A063997/4 and A279769 (the analog for 9).

Cf. A007953 (digital sum), A279772 (sumdigits(2n) = 4), A279773 (sumdigits(3n) = 6), A279775 (sumdigits(5n) = 10), A279776 (sumdigits(6n) = 12), A279770 (sumdigits(7n) = 14), A279768 (sumdigits(8n) = 16), A279769 (sumdigits(9n) = 18), A279777 (sumdigits(9n) = 27).
Digital sum of m*n equals m: A088404 = A069537/2, A088405 = A052217/3, A088406 = A063997/4, A088407 = A069540/5, A088408 = A062768/6, A088409 = A063416/7, A088410 = A069543/8.
Cf. A005349 (Niven or Harshad numbers), A245062 (arranged in rows by digit sums).
Numbers with given digital sum: A011557 (1), A052216 (2), A052217 (3), A052218 (4), A052219 (5), A052220 (6), A052221 (7), A052222 (8), A052223 (9), A052224 (10), A166311 (11), A235151 (12), A143164 (13), A235225 (14), A235226 (15), A235227 (16), A166370 (17), A235228 (18), A166459 (19), A235229 (20).

Select[Range@ 2000, Total@ IntegerDigits[4 #] == 8 &] (* Michael De Vlieger, Dec 23 2016 *)

select( is(n)=sumdigits(4*n)==8, [1..1999])

A279776 Numbers n such that the sum of digits of 6n equals 12.

Original entry on oeis.org

8, 11, 14, 23, 26, 29, 32, 38, 41, 44, 47, 53, 56, 59, 62, 65, 68, 71, 74, 77, 80, 86, 89, 92, 95, 101, 104, 107, 110, 119, 122, 125, 134, 137, 140, 152, 155, 173, 176, 179, 182, 188, 191, 194, 197, 203, 206, 209, 212, 215, 218, 221, 224, 227, 230, 236

Offset: 1

M. F. Hasler, Dec 23 2016

Inspired by A088408 = A062768/6 and A279769 (the analog for 9).

Cf. A007953 (digital sum), A279772 (sumdigits(2n) = 4), A279773 (sumdigits(3n) = 6), A279774 (sumdigits(4n) = 8), A279775 (sumdigits(5n) = 10), A279770 (sumdigits(7n) = 14), A279768 (sumdigits(8n) = 16), A279769 (sumdigits(9n) = 18), A279777 (sumdigits(9n) = 27).
Digital sum of m*n equals m: A088404 = A069537/2, A088405 = A052217/3, A088406 = A063997/4, A088407 = A069540/5, A088408 = A062768/6, A088409 = A063416/7, A088410 = A069543/8.
Cf. A005349 (Niven or Harshad numbers), A245062 (arranged in rows by digit sums).
Numbers with given digital sum: A011557 (1), A052216 (2), A052217 (3), A052218 (4), A052219 (5), A052220 (6), A052221 (7), A052222 (8), A052223 (9), A052224 (10), A166311 (11), A235151 (12), A143164 (13), A235225 (14), A235226 (15), A235227 (16), A166370 (17), A235228 (18), A166459 (19), A235229 (20).

Select[Range@ 240, Total@ IntegerDigits[6 #] == 12 &] (* Michael De Vlieger, Dec 23 2016 *)

PARI
```
is(n)=sumdigits(6*n)==12
```

A279771 Numbers n such that the sum of digits of 11n equals 11.

Original entry on oeis.org

19, 28, 37, 46, 55, 64, 73, 82, 190, 280, 370, 460, 550, 640, 730, 820, 919, 928, 937, 946, 955, 964, 973, 982, 991, 1819, 1828, 1837, 1846, 1855, 1864, 1873, 1882, 1891, 1900, 2728, 2737, 2746, 2755, 2764, 2773, 2782, 2791, 2800, 3637, 3646, 3655, 3664

Offset: 1

M. F. Hasler, Dec 23 2016

Inspired by A088404 = A069537/2 through A088410 = A069543/8.

Cf. A007953 (digital sum), Digital sum of m*n equals m: A088404 = A069537/2, A088405 = A052217/3, A088406 = A063997/4, A088407 = A069540/5, A088408 = A062768/6, A088409 = A063416/7, A088410 = A069543/8.
Cf. A005349 (Niven or Harshad numbers), A245062 (arranged in rows by digit sums).
Numbers with given digital sum: A011557 (1), A052216 (2), A052217 (3), A052218 (4), A052219 (5), A052220 (6), A052221 (7), A052222 (8), A052223 (9), A052224 (10), A166311 (11), A235151 (12), A143164 (13), A235225 (14), A235226 (15), A235227 (16), A166370 (17), A235228 (18), A166459 (19), A235229 (20).
Cf. A279772 (sumdigits(2n) = 4), A279773 (sumdigits(3n) = 6), A279774 (sumdigits(4n) = 8), A279775 (sumdigits(5n) = 10), A279776 (sumdigits(6n) = 12), A279770 (sumdigits(7n) = 14), A279768 (sumdigits(8n) = 16), A279769 (sumdigits(9n) = 18), A279777 (sumdigits(9n) = 27).

Select[Range@ 3664, Total@IntegerDigits[11 #] == 11 &] (* Michael De Vlieger, Dec 23 2016 *)

PARI
```
is(n)=sumdigits(11*n)==11
```

cp's OEIS Frontend

A235228 Numbers whose sum of digits is 18.

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A279777 Numbers k such that the sum of digits of 9k is 27.

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A279768 Numbers n such that the sum of digits of 8n equals 16.

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A279775 Numbers k such that the sum of digits of 5k equals 10.

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A279770 Numbers n such that the sum of digits of 7n equals 14.

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A279772 Numbers n such that the sum of digits of 2n equals 4.

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A279773 Numbers n such that the sum of digits of 3n equals 6.

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A279774 Numbers n such that the sum of digits of 4n equals 8.

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A279776 Numbers n such that the sum of digits of 6n equals 12.

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