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Search: id:A096091
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| A096091 |
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k such that f(k) mod g(k) = 0, where f(k) = largest number formed using digits of k, g(k) = smallest number formed using digits of k. |
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+0
3
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| 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 20, 22, 30, 33, 40, 44, 50, 55, 60, 66, 70, 77, 80, 88, 90, 99, 100, 110, 111, 200, 220, 222, 300, 330, 333, 400, 440, 444, 500, 510, 540, 550, 555, 600, 660, 666, 700, 770, 777, 800, 810, 880, 888, 900, 990, 999, 1000, 1001, 1100
(list; graph; listen)
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OFFSET
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1,2
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COMMENT
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All palindromes are trivial members. N = d*10^m*(10^n-1)/9 is a member for all m, n where 1 < d < 10. And one gets f(N)/g(N) = 10^m. e.g. for d= 7 m = 4, n = 8 we get N = 777777770000. Conjecture: There are infinitely many terms other than these.
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EXAMPLE
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110 is a member as 110/011=10.
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MATHEMATICA
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f[n_] := Block[{p = FromDigits /@ Permutations[IntegerDigits[n]]}, Mod[ p[[1]], p[[ -1]] ]]; Select[ Range[1111], f[ # ] == 0 &] (from Robert G. Wilson v Jun 23 2004)
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CROSSREFS
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Cf. A096089, A096090.
Sequence in context: A084050 A061917 A125289 this_sequence A055933 A132578 A101318
Adjacent sequences: A096088 A096089 A096090 this_sequence A096092 A096093 A096094
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KEYWORD
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base,nonn
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AUTHOR
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Amarnath Murthy (amarnath_murthy(AT)yahoo.com), Jun 22 2004
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EXTENSIONS
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Edited, corrected and extended by Robert G. Wilson v (rgwv(AT)rgwv.com), Jun 23 2004
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