A053654 -id:A053654 - cp's OEIS frontend

A161750 Numbers n such that the decimal digits of 123456789*n are all distinct.

0, 1, 2, 4, 5, 7, 8, 10, 11, 13, 14, 16, 17, 20, 22, 23, 25, 26, 31, 32, 34, 35, 40, 41, 43, 44, 50, 52, 53, 61, 62, 70, 71, 80

Offset: 1

Kyle Stern, Jun 17 2009

David Wolfe, When Multiplication Mixes Up Digits, Mathematics Magazine, Volume 80, Number 5, December 2007, pp.380-383

Cf. A053654. [From Zak Seidov, Nov 04 2009]

a := proc (n) local nn, nnn: nn := convert(123456789*n, base, 10): nnn := convert(nn, set): if nops(nn) = nops(nnn) then n else end if end proc: seq(a(n), n = 1 .. 80); # Emeric Deutsch, Jun 21 2009

m=123456789;se=Select[Range[0,99],Sort[id=IntegerDigits[m*# ]]==Union[id]&] (* Zak Seidov, Nov 04 2009 *)
Select[Range[0,100],Max[DigitCount[123456789#]]==1&] (* Harvey P. Dale, Jun 02 2017 *)

a(1)=0 added by Zak Seidov, Nov 04 2009

Edited by Charles R Greathouse IV, Aug 02 2010

A167461 Anagram multiples of 123456789.

Original entry on oeis.org

1234567890, 1358024679, 1604938257, 1728395046, 1975308624, 2098765413, 2469135780, 2716049358, 2839506147, 3086419725, 3209876514, 3827160459, 3950617248, 4197530826, 4320987615, 4938271560, 5061728349, 5308641927

Offset: 1

Zak Seidov, Nov 04 2009

There are exactly 27 all_ten_distinct_digit numbers divisible by 123456789:
1234567890, 1358024679, 1604938257, 1728395046, 1975308624, 2098765413,
2469135780, 2716049358, 2839506147, 3086419725, 3209876514, 3827160459,
3950617248, 4197530826, 4320987615, 4938271560, 5061728349, 5308641927,
5432098716, 6172839450, 6419753028, 6543209817, 7530864129, 7654320918,
8641975230, 8765432019, 9876543120.

Cf. A050278 (Pandigital numbers: numbers containing the digits 0-9), A053654, A161750.

A167476 Pandigital numbers n with at least 4 nontrivial anagrams divisible by n.

Original entry on oeis.org

1039675824, 1053826974, 1068253974, 1068379524, 1073968254, 1075396824, 1098765432, 1204756839, 1234567890, 1357802469

Offset: 1

Zak Seidov, Nov 04 2009

For a(7) and a(9), there are 5 nontrivial anagrams divisible by n.
List of anagrams:
{1039675824,2079351648,4158703296,8317406592,9357082416},
{1053826974,2107653948,4215307896,5269134870,8430615792},
{1068253974,2136507948,4273015896,5341269870,8546031792},
{1068379524,2136759048,4273518096,5341897620,8547036192},
{1073968254,2147936508,4295873016,5369841270,8591746032},
{1075396824,2150793648,4301587296,5376984120,8603174592},
{1098765432,2197530864,4395061728,5493827160,7691358024,8790123456},
{1204756839,2409513678,4819027356,6023784195,9638054712},
{1234567890,2469135780,4938271560,6172839450,8641975230,9876543120},
{1357802469,2715604938,5431209876,6789012345,9504617283}.

			a(1)=1039675824 with 4 anagram multiples:
2*a(1)=2079351648, 4*a(1)=4158703296, 8*a(1)=8317406592, 9*a(1)=9357082416;
a(2)=1053826974 with 4 anagram multiples:
2*a(2)=2107653948, 4*a(2)=4215307896, 5*a(2)=5269134870, 8*a(2)=8430615792.

Cf. A050278, A053654, A161750, A167461.

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A161750 Numbers n such that the decimal digits of 123456789*n are all distinct.

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A167461 Anagram multiples of 123456789.

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A167476 Pandigital numbers n with at least 4 nontrivial anagrams divisible by n.

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