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 A246535 Largest number with at most n distinct digits in any base b >= 2 (written in decimal). 1
 1, 43, 2462, 140081, 20338085, 2610787117 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,2 COMMENTS a(n) is the last occurrence of n in A037968. a(n) >= A049363(n+1) - 1 for all n. - Derek Orr, Aug 31 2014 From Derek Orr, Aug 31 2014 (Start): At least for 1 <= n <= 5, a(n)+1 fails when written in base n^2+1. Examples: a(1) = 1 written in base 2 is 1 (1 distinct digit). 2 written in base (2-1)^2+1 = 2 is 10. Thus 2 fails. a(2) = 43 written in base 3 is 1121 (2 distinct digits). 44 written in base 2^2+1 = 5 is 134. Thus 44 fails. a(3) = 2462 written in base 4 is 212132 (3 distinct digits). 2463 written in base 3^2+1 = 10 is 2463. Thus 2463 fails. Generalizing... (Conjecture) a(n) written in base n+1 has n distinct digits. a(n)+1 written in base n^2+1 will always have n+1 distinct digits. Further, for 1 < n <= 5, a(n)-1 fails when written in base n^2+1. (End) a(1)-a(6) are confirmed for all n <= 10^11. - Hiroaki Yamanouchi, Sep 21 2014 a(6) = 2610787117 written in base 7 is 121461216151 (5 distinct digits), and 2610787118 written in base 6^2+1 = 37 is (1)(0)(24)(1)(22)(2)(0) (5 distinct digits). Therefore, Derek Orr's conjecture seems to be wrong. a(7) >= 314941024802. - Hiroaki Yamanouchi, Sep 21 2014 LINKS EXAMPLE a(2) = 43 since 43 has two distinct digits in bases 2 <= b <= 5, 7 <= b <= 41 and b = 43, and one distinct digit in bases b = 6, b = 42 and b >= 44. All greater numbers have at least 3 distinct digits in some base b >= 2. CROSSREFS Cf. A037968. Sequence in context: A076572 A015258 A130014 * A265234 A015323 A145315 Adjacent sequences:  A246532 A246533 A246534 * A246536 A246537 A246538 KEYWORD nonn,base,hard,more AUTHOR Joonas Pohjonen, Aug 28 2014 EXTENSIONS a(6) from Hiroaki Yamanouchi, Sep 21 2014 STATUS approved

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Last modified May 14 16:23 EDT 2021. Contains 343884 sequences. (Running on oeis4.)