# Numbers Whose Digits Add Up to n

Contents

## Introduction

Numbers from 1 to 1,000 whose digits add up to n.

\\ PARI/GP
n = 1;
for (x = 1, 1000, if (vecsum(digits(x)) == n, print1(x, “, “)));

1, 10, 100, 1000

## Digits Add Up to 2

2, 11, 20, 101, 110, 200

## Digits Add Up to 3

3, 12, 21, 30, 102, 111, 120, 201, 210, 300

## Digits Add Up to 4

4, 13, 22, 31, 40, 103, 112, 121, 130, 202, 211, 220, 301, 310, 400

## Digits Add Up to 5

5, 14, 23, 32, 41, 50, 104, 113, 122, 131, 140, 203, 212, 221, 230, 302, 311, 320, 401, 410, 500

### Numbers from 1 to 1,000,000

5, 14, 23, 32, 41, 50, 104, 113, 122, 131, 140, 203, 212, 221, 230, 302, 311, 320, 401, 410, 500, 1004, 1013, 1022, 1031, 1040, 1103, 1112, 1121, 1130, 1202, 1211, 1220, 1301, 1310, 1400, 2003, 2012, 2021, 2030, 2102, 2111, 2120, 2201, 2210, 2300, 3002, 3011, 3020, 3101, 3110, 3200, 4001, 4010, 4100, 5000, 10004, 10013, 10022, 10031, 10040, 10103, 10112, 10121, 10130, 10202, 10211, 10220, 10301, 10310, 10400, 11003, 11012, 11021, 11030, 11102, 11111, 11120, 11201, 11210, 11300, 12002, 12011, 12020, 12101, 12110, 12200, 13001, 13010, 13100, 14000, 20003, 20012, 20021, 20030, 20102, 20111, 20120, 20201, 20210, 20300, 21002, 21011, 21020, 21101, 21110, 21200, 22001, 22010, 22100, 23000, 30002, 30011, 30020, 30101, 30110, 30200, 31001, 31010, 31100, 32000, 40001, 40010, 40100, 41000, 50000, 100004, 100013, 100022, 100031, 100040, 100103, 100112, 100121, 100130, 100202, 100211, 100220, 100301, 100310, 100400, 101003, 101012, 101021, 101030, 101102, 101111, 101120, 101201, 101210, 101300, 102002, 102011, 102020, 102101, 102110, 102200, 103001, 103010, 103100, 104000, 110003, 110012, 110021, 110030, 110102, 110111, 110120, 110201, 110210, 110300, 111002, 111011, 111020, 111101, 111110, 111200, 112001, 112010, 112100, 113000, 120002, 120011, 120020, 120101, 120110, 120200, 121001, 121010, 121100, 122000, 130001, 130010, 130100, 131000, 140000, 200003, 200012, 200021, 200030, 200102, 200111, 200120, 200201, 200210, 200300, 201002, 201011, 201020, 201101, 201110, 201200, 202001, 202010, 202100, 203000, 210002, 210011, 210020, 210101, 210110, 210200, 211001, 211010, 211100, 212000, 220001, 220010, 220100, 221000, 230000, 300002, 300011, 300020, 300101, 300110, 300200, 301001, 301010, 301100, 302000, 310001, 310010, 310100, 311000, 320000, 400001, 400010, 400100, 401000, 410000, 500000

## Digits Add Up to 6

6, 15, 24, 33, 42, 51, 60, 105, 114, 123, 132, 141, 150, 204, 213, 222, 231, 240, 303, 312, 321, 330, 402, 411, 420, 501, 510, 600

## Digits Add Up to 7

7, 16, 25, 34, 43, 52, 61, 70, 106, 115, 124, 133, 142, 151, 160, 205, 214, 223, 232, 241, 250, 304, 313, 322, 331, 340, 403, 412, 421, 430, 502, 511, 520, 601, 610, 700

## Digits Add Up to 8

8, 17, 26, 35, 44, 53, 62, 71, 80, 107, 116, 125, 134, 143, 152, 161, 170, 206, 215, 224, 233, 242, 251, 260, 305, 314, 323, 332, 341, 350, 404, 413, 422, 431, 440, 503, 512, 521, 530, 602, 611, 620, 701, 710, 800

## Digits Add Up to 9

9, 18, 27, 36, 45, 54, 63, 72, 81, 90, 108, 117, 126, 135, 144, 153, 162, 171, 180, 207, 216, 225, 234, 243, 252, 261, 270, 306, 315, 324, 333, 342, 351, 360, 405, 414, 423, 432, 441, 450, 504, 513, 522, 531, 540, 603, 612, 621, 630, 702, 711, 720, 801, 810, 900

## Digits Add Up to 10

19, 28, 37, 46, 55, 64, 73, 82, 91, 109, 118, 127, 136, 145, 154, 163, 172, 181, 190, 208, 217, 226, 235, 244, 253, 262, 271, 280, 307, 316, 325, 334, 343, 352, 361, 370, 406, 415, 424, 433, 442, 451, 460, 505, 514, 523, 532, 541, 550, 604, 613, 622, 631, 640, 703, 712, 721, 730, 802, 811, 820, 901, 910

## Digits Add Up to 11

29, 38, 47, 56, 65, 74, 83, 92, 119, 128, 137, 146, 155, 164, 173, 182, 191, 209, 218, 227, 236, 245, 254, 263, 272, 281, 290, 308, 317, 326, 335, 344, 353, 362, 371, 380, 407, 416, 425, 434, 443, 452, 461, 470, 506, 515, 524, 533, 542, 551, 560, 605, 614, 623, 632, 641, 650, 704, 713, 722, 731, 740, 803, 812, 821, 830, 902, 911, 920

## Digits Add Up to 12

39, 48, 57, 66, 75, 84, 93, 129, 138, 147, 156, 165, 174, 183, 192, 219, 228, 237, 246, 255, 264, 273, 282, 291, 309, 318, 327, 336, 345, 354, 363, 372, 381, 390, 408, 417, 426, 435, 444, 453, 462, 471, 480, 507, 516, 525, 534, 543, 552, 561, 570, 606, 615, 624, 633, 642, 651, 660, 705, 714, 723, 732, 741, 750, 804, 813, 822, 831, 840, 903, 912, 921, 930

## Digits Add Up to 13

49, 58, 67, 76, 85, 94, 139, 148, 157, 166, 175, 184, 193, 229, 238, 247, 256, 265, 274, 283, 292, 319, 328, 337, 346, 355, 364, 373, 382, 391, 409, 418, 427, 436, 445, 454, 463, 472, 481, 490, 508, 517, 526, 535, 544, 553, 562, 571, 580, 607, 616, 625, 634, 643, 652, 661, 670, 706, 715, 724, 733, 742, 751, 760, 805, 814, 823, 832, 841, 850, 904, 913, 922, 931, 940

## Digits Add Up to 14

59, 68, 77, 86, 95, 149, 158, 167, 176, 185, 194, 239, 248, 257, 266, 275, 284, 293, 329, 338, 347, 356, 365, 374, 383, 392, 419, 428, 437, 446, 455, 464, 473, 482, 491, 509, 518, 527, 536, 545, 554, 563, 572, 581, 590, 608, 617, 626, 635, 644, 653, 662, 671, 680, 707, 716, 725, 734, 743, 752, 761, 770, 806, 815, 824, 833, 842, 851, 860, 905, 914, 923, 932, 941, 950

## Digits Add Up to 15

69, 78, 87, 96, 159, 168, 177, 186, 195, 249, 258, 267, 276, 285, 294, 339, 348, 357, 366, 375, 384, 393, 429, 438, 447, 456, 465, 474, 483, 492, 519, 528, 537, 546, 555, 564, 573, 582, 591, 609, 618, 627, 636, 645, 654, 663, 672, 681, 690, 708, 717, 726, 735, 744, 753, 762, 771, 780, 807, 816, 825, 834, 843, 852, 861, 870, 906, 915, 924, 933, 942, 951, 960

## Digits Add Up to 16

79, 88, 97, 169, 178, 187, 196, 259, 268, 277, 286, 295, 349, 358, 367, 376, 385, 394, 439, 448, 457, 466, 475, 484, 493, 529, 538, 547, 556, 565, 574, 583, 592, 619, 628, 637, 646, 655, 664, 673, 682, 691, 709, 718, 727, 736, 745, 754, 763, 772, 781, 790, 808, 817, 826, 835, 844, 853, 862, 871, 880, 907, 916, 925, 934, 943, 952, 961, 970

## Digits Add Up to 17

89, 98, 179, 188, 197, 269, 278, 287, 296, 359, 368, 377, 386, 395, 449, 458, 467, 476, 485, 494, 539, 548, 557, 566, 575, 584, 593, 629, 638, 647, 656, 665, 674, 683, 692, 719, 728, 737, 746, 755, 764, 773, 782, 791, 809, 818, 827, 836, 845, 854, 863, 872, 881, 890, 908, 917, 926, 935, 944, 953, 962, 971, 980

## Digits Add Up to 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, 972, 981, 990

## Digits Add Up to 19

199, 289, 298, 379, 388, 397, 469, 478, 487, 496, 559, 568, 577, 586, 595, 649, 658, 667, 676, 685, 694, 739, 748, 757, 766, 775, 784, 793, 829, 838, 847, 856, 865, 874, 883, 892, 919, 928, 937, 946, 955, 964, 973, 982, 991

## Digits Add Up to 20

299, 389, 398, 479, 488, 497, 569, 578, 587, 596, 659, 668, 677, 686, 695, 749, 758, 767, 776, 785, 794, 839, 848, 857, 866, 875, 884, 893, 929, 938, 947, 956, 965, 974, 983, 992

## Digits Add Up to 21

399, 489, 498, 579, 588, 597, 669, 678, 687, 696, 759, 768, 777, 786, 795, 849, 858, 867, 876, 885, 894, 939, 948, 957, 966, 975, 984, 993

## Digits Add Up to 22

499, 589, 598, 679, 688, 697, 769, 778, 787, 796, 859, 868, 877, 886, 895, 949, 958, 967, 976, 985, 994

## Digits Add Up to 23

599, 689, 698, 779, 788, 797, 869, 878, 887, 896, 959, 968, 977, 986, 995

## Digits Add Up to 24

699, 789, 798, 879, 888, 897, 969, 978, 987, 996

## Digits Add Up to 25

799, 889, 898, 979, 988, 997

899, 989, 998

999

## Digits Add Up to 28

There are no numbers from 1 to 1,000 that fit the pattern.