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 A363160 Smallest positive integer m with all digits distinct such that m^n contains each digit of m exactly n times, or -1 if no such m exists. 0
 1, 406512, 516473892, 5702631489, 961527834, 7025869314, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,2 COMMENTS For 7 <= n <= 185, I tried all possibilities with at most 10 distinct digits and I found no solution. 9876543210^186 has only 1859 < 186 * 10 = 1860 digits, so a(n) = -1 for n = 186. So 9876543210^n has fewer than 10*n digits for n >= 186, so a(n) = -1 for n >= 186. LINKS Table of n, a(n) for n=1..59. EXAMPLE a(1) = 1, because 1^1 = 1 has each digit of 1, 1 time, and no lesser number > 0 satisfies this. a(2) = 406512, because 406512 has distinct digits, 406512^2 = 165252006144 has each digit of 406512, 2 times, and no lesser number satisfies this. n a(n) a(n)^n 1 1 1 2 406512 165252006144 3 516473892 137766973511455269432948288 4 5702631489 1057550783692741389295697108242363408641 5 961527834 821881685441327565743977956591832631269739424 6 7025869314 120281934463386157260042215510596389732740014997586987548736 MATHEMATICA hasDistinctDigitsQ[m_Integer?NonNegative]:=Length@IntegerDigits@m==Length@DeleteDuplicates@IntegerDigits@m; validNumberQ[n_Integer?NonNegative, m_Integer?NonNegative]:=AllTrue[Tally@IntegerDigits@m, Function[{digitFreq}, MemberQ[Tally@IntegerDigits[m^n], {digitFreq[[1]], n*digitFreq[[2]]}]]]; a[n_Integer?Positive, ex_Integer?Positive]:=Module[{m=1}, Monitor[While[True, If[hasDistinctDigitsQ[m]&&validNumberQ[n, m], Return[m]]; m++; If[m>10^(ex*n), Return[-1]]; ]; m, m]]; Table[a[n, 7], {n, 1, 7}] (* Robert P. P. McKone, Sep 09 2023 *) CROSSREFS Cf. A114258, A114259, A114260, A114261, A199630, A199631, A199632, A199633, A365144, A114260. Sequence in context: A237510 A234375 A237919 * A210265 A043609 A220988 Adjacent sequences: A363157 A363158 A363159 * A363161 A363162 A363163 KEYWORD sign,base AUTHOR Jean-Marc Rebert, Sep 07 2023 STATUS approved

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Last modified February 28 21:38 EST 2024. Contains 370400 sequences. (Running on oeis4.)