A241146 Least number k such that k and n*k share at least one digit.

1, 10, 5, 10, 5, 2, 5, 10, 5, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 10, 1, 9, 5, 10, 5, 2, 5, 6, 5, 5, 1, 10, 5, 10, 4, 2, 4, 10, 5, 10, 1, 10, 5, 3, 3, 2, 5, 8, 5, 5, 1, 10, 5, 7, 5, 2, 5, 10, 5, 2, 1, 2, 2, 2, 5, 2, 5, 7, 5, 5, 1, 10, 5, 10, 5, 2, 3, 3, 3, 10, 1, 7, 5, 10, 4, 2, 4, 9, 5, 5, 1, 10, 5, 6, 5, 2, 5, 8, 5, 1

Offset: 1

Author

Robert G. Wilson v, Apr 16 2014

Keywords

• nonn
• base
• easy

Comments

\ 10^3...10^4....10^5.....10^6......10^7.......10^8........10^9

k\

.1..272...3440...40952...468560...5217032...56953280...612579512

.2..149...1613...16837...171325...1710773...16837421...163825573

.3...87...1091...12038...124060...1225493...11762254...110573419

.4...62....710....7196....68280....621670....5502346....47710882

.5..248...1914...14674...111846....848318....6407338....48220222

.6...26....246....2087....16749....129768.....980911.....7280424

.7...36....323....2587....19368....138838.....966609.....6591845

.8...20....156....1095.....7199.....45386.....277985.....1667513

.9...22....162....1028.....6055.....34178.....187661.....1010240

10...78....345....1506.....6558.....28544.....124195......540370

The sequence of numbers whose first digit is k:

.1: 1, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 21, 31, 41, 51, 61, 71, 81, 91, 100, …, . A011531?

.2: 6, 26, 36, 46, 56, 60, 62, 63, 64, 66, 76, 86, 96, 206, 226, 236, 246, 256, 260, 262, …, .

.3: 44, 45, 77, 78, 79, 244, 245, 277, 278, 279, 344, 345, 377, 378, 379, 434, 435, 437, 438, …, .

.4: 35, 37, 85, 87, 235, 237, 285, 287, 335, 337, 350, 352, 353, 354, 355, 357, 358, 359, 365, …, .

.5: 3, 5, 7, 9, 23, 25, 27, 29, 30, 33, 39, 43, 47, 49, 50, 53, 55, 57, 59, 65, 67, 69, 70, 73, …, .

.6: 28, 94, 228, 268, 272, 274, 280, 282, 294, 328, 394, 428, 494, 528, 594, 694, 728, 828, 894, …, .

.7: 54, 68, 82, 248, 252, 254, 382, 388, 392, 398, 468, 482, 532, 534, 538, 540, 542, 554, 568, …, .

.8: 48, 98, 232, 234, 298, 348, 480, 484, 498, 548, 598, 698, 732, 734, 748, 848, 898, 980, 984, …, .

.9: 22, 88, 220, 222, 288, 322, 324, 332, 422, 488, 522, 552, 588, 658, 688, 722, 880, 884, 888, …, .

10: 2, 4, 8, 20, 24, 32, 34, 38, 40, 42, 52, 58, 72, 74, 80, 84, 92, 200, 202, 204, 208, 224, …, .

Crossrefs

Cf. A129845, A129846, A129848, A241141, A241142, A241143, A241144, A241145.

Programs

Mathematica

f[n_] := Block[{k = 1}, While[ Intersection[ IntegerDigits[k], IntegerDigits[n*k]] == {}, k++]; k]; Array[f, 100]

Formula

If a(n) = k so does a(10n).