A129846 -id:A129846 - cp's OEIS frontend

A241142 Numbers n such that n and 6n share at least one digit.

2, 4, 6, 8, 10, 12, 14, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 30, 31, 32, 34, 36, 38, 39, 40, 41, 42, 44, 46, 48, 49, 50, 52, 53, 54, 56, 58, 59, 60, 61, 62, 63, 64, 66, 68, 70, 72, 73, 74, 75, 76, 78, 79, 80, 81, 82, 83, 84, 85, 86, 88, 90, 92, 94, 95, 96, 98, 99, 100

Offset: 1

Robert G. Wilson v, Apr 16 2014

All numbers n which are congruent to 0 (mod 6) have this characteristic.

All even n have this characteristic, because n == 6n mod 10. Robert Israel, Apr 17 2014

			12 is in the sequence since 12 and 6*12 = 72 and together they share the digit 2.

Robert Israel, Table of n, a(n) for n = 1..10000

Cf. A129845, A129846, A129848, A241141, A241143, A241144, A241145, A241146.

  N:= 10000;  # to get all entries up to N
filter:= proc(n) local L, L6;
   L:= convert(convert(n,base,10),set);
   L6:= convert(convert(6*n,base,10),set);
   L intersect L6 <> {};
end;
select(filter, [$1..N]); # Robert Israel, Apr 17 2014

fQ[n_] := Intersection[ IntegerDigits[ n], IntegerDigits[6 n]] != {}; Select[ Range[ 100], fQ]

isok(n) = #setintersect(Set(digits(n)), Set(digits(6*n))); \\ Michel Marcus, Apr 17 2014

A241141 Numbers n such that n and 5n share at least one digit.

Original entry on oeis.org

5, 10, 15, 19, 20, 21, 24, 25, 30, 31, 35, 39, 40, 42, 45, 48, 49, 50, 51, 52, 53, 55, 57, 59, 60, 63, 65, 70, 73, 74, 75, 79, 80, 84, 85, 90, 94, 95, 98, 99, 100, 101, 102, 103, 104, 105, 106, 108, 110, 115, 119, 120, 122, 123, 124, 125, 126, 130, 135, 136, 139, 140, 142, 143, 145, 147, 148, 149, 150, 151, 153

Offset: 1

Robert G. Wilson v, Apr 16 2014

All numbers n which are congruent to 0 (mod 5) have this characteristic.

			19 is in the sequence since 19 and 5*19 = 95 and together they share the digit 9.

Cf. A129845, A129846, A129848, A241142, A241143, A241144, A241145, A241146.

fQ[n_] := Intersection[ IntegerDigits[ n], IntegerDigits[5 n]] != {} && Mod[n, 5] != 0; Select[ Range[ 100], fQ]

isok(n) = #setintersect(Set(digits(n)), Set(digits(5*n))); \\ Michel Marcus, Apr 17 2014

A241143 Numbers n such that n and 7n share at least one digit.

Original entry on oeis.org

5, 10, 13, 15, 16, 17, 18, 19, 20, 21, 25, 26, 29, 30, 31, 32, 33, 34, 35, 39, 40, 42, 43, 45, 49, 50, 51, 53, 55, 60, 64, 65, 66, 67, 68, 70, 71, 75, 80, 83, 84, 85, 86, 90, 95, 96, 97, 98, 99, 100, 101, 102, 103, 105, 107, 110, 113, 115, 116, 117, 118, 120, 123, 125, 126, 128, 129, 130, 131, 132, 133, 134, 135, 139, 140

Offset: 1

Robert G. Wilson v, Apr 16 2014

All numbers n which are congruent to 0 (mod 5) have this characteristic.

			13 is in the sequence since 13 and 7*13 = 91 and together they share the digit 1.

Cf. A129845, A129846, A129848, A241141, A241142, A241144, A241145, A241146.

fQ[n_] := Intersection[ IntegerDigits[ n], IntegerDigits[7 n]] != {}; Select[ Range[ 100], fQ]

A241144 Numbers n such that n and 8n share at least one digit.

Original entry on oeis.org

10, 13, 14, 15, 16, 17, 18, 19, 20, 21, 24, 25, 26, 27, 28, 29, 30, 32, 38, 39, 40, 43, 46, 47, 48, 49, 50, 54, 57, 60, 62, 65, 67, 70, 72, 76, 80, 81, 85, 86, 90, 96, 97, 98, 99, 100, 101, 102, 105, 108, 110, 114, 119, 120, 124, 125, 126, 127, 128, 129, 130, 131, 132, 133, 134, 135, 136, 137, 138, 139, 140, 141

Offset: 1

Robert G. Wilson v, Apr 16 2014

			13 is in the sequence since 13 and 8*13 = 104 and together they share the digit 1.

Cf. A129845, A129846, A129848, A241141, A241142, A241143, A241145, A241146.

fQ[n_] := Intersection[ IntegerDigits[ n], IntegerDigits[8 n]] != {}; Select[ Range[ 140], fQ]

A241145 Numbers n such that n and 9n share at least one digit.

Original entry on oeis.org

5, 10, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 23, 24, 25, 26, 27, 28, 29, 30, 32, 34, 35, 36, 37, 38, 39, 40, 43, 45, 46, 47, 48, 49, 50, 51, 54, 55, 56, 57, 58, 59, 60, 63, 64, 65, 67, 68, 69, 70, 73, 75, 76, 78, 79, 80, 82, 85, 87, 89, 90, 91, 92, 93, 94, 95, 96, 97, 98, 99, 100, 101, 102, 105, 109, 110, 112, 113

Offset: 1

Robert G. Wilson v, Apr 16 2014

			13 is in the sequence since 13 and 8*13 = 104 and together they share the digit 1.

Cf. A129845, A129846, A129848, A241141, A241142, A241143, A241144, A241146.

fQ[n_] := Intersection[ IntegerDigits[ n], IntegerDigits[9 n]] != {}; Select[ Range[ 115], fQ]

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

Original entry on oeis.org

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

Robert G. Wilson v, Apr 16 2014

\ 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, …, .

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

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

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

A140467 Numbers k such that the digits of k are not present in 3k.

Original entry on oeis.org

1, 2, 3, 4, 6, 7, 8, 9, 11, 12, 16, 18, 19, 21, 22, 23, 26, 27, 29, 32, 33, 34, 36, 37, 38, 39, 43, 44, 46, 54, 58, 59, 63, 64, 66, 67, 68, 69, 73, 74, 76, 77, 78, 81, 83, 84, 87, 88, 89, 91, 94, 96, 108, 109, 111, 112, 116, 118, 119, 121, 122, 126, 129, 136, 158, 159, 161

Offset: 1

Jonathan Vos Post, Jun 25 2008

			169 is in the sequence because the sets {1,6,9} and {5,0,7} are disjoint.

Robert Israel, Table of n, a(n) for n = 1..10000

Complement of A129846.

a:=proc(n) local nd, n3d: nd:=convert(convert(n,base,10),set): n3d:=convert(convert(3*n,base,10),set): if `intersect`(nd, n3d)={} then n else end if end proc: seq(a(n),n=1..170); # Emeric Deutsch, Jul 20 2008

Select[Range[200],Intersection[IntegerDigits[#],IntegerDigits[3*#]]=={}&] (* Harvey P. Dale, Aug 13 2018 *)

More terms from Emeric Deutsch, Jul 20 2008

cp's OEIS Frontend

A241142 Numbers n such that n and 6n share at least one digit.

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A241141 Numbers n such that n and 5n share at least one digit.

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A241143 Numbers n such that n and 7n share at least one digit.

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A241144 Numbers n such that n and 8n share at least one digit.

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A241145 Numbers n such that n and 9n share at least one digit.

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

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A140467 Numbers k such that the digits of k are not present in 3k.

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