A129845 -id:A129845 - 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).

A038365 Numbers n with property that digits of n are not present in 2n.

Original entry on oeis.org

1, 2, 3, 4, 5, 6, 7, 8, 9, 11, 13, 14, 15, 16, 17, 18, 19, 22, 23, 27, 28, 29, 31, 32, 33, 34, 35, 36, 38, 39, 41, 43, 44, 45, 46, 48, 52, 53, 54, 55, 56, 57, 58, 59, 64, 65, 66, 67, 69, 72, 73, 76, 77, 78, 79, 82, 83, 85, 86, 88, 92, 93, 94, 111, 113, 114, 115, 116, 117, 118

Offset: 1

Erich Friedman

207 is the smallest number containing a zero, cf. A192825. [Reinhard Zumkeller, Aug 09 2011]

			36 is in the list since 2*36=72, which shares no digit with 36.

T. D. Noe, Table of n, a(n) for n=1..2000

Cf. A129845 (complement).

import Data.List (intersect)
a038365 n = a038365_list !! (n-1)
a038365_list = filter (\x -> null (show (2*x) `intersect` show x)) [1..]
-- Reinhard Zumkeller, Aug 09 2011

Select[Range[140],Intersection[IntegerDigits[2 #], IntegerDigits[#]] =={}&]  (* Harvey P. Dale, Apr 30 2011 *)

cp's OEIS Frontend

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

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Maple

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

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PARI

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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A038365 Numbers n with property that digits of n are not present in 2n.

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