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 A330083 a(n) is the smallest number k > 0 such that for each b = 2..n the base-b expansion of k has exactly n - b zeros. 0
 1, 2, 10, 18, 271 (list; graph; refs; listen; history; text; internal format)
 OFFSET 2,2 COMMENTS This list is complete. Proof: When converting base 2 to base 4, we can group the digits in base 2 into pairs from the least significant bit. We then convert pairs into single digits in base 4 as 00 -> 0, 01 -> 1, 10 -> 2, 11 -> 3. This always causes the number of zeros to go to half or less than half. For all n >= 7, n-4 is greater than (n-2)/2, so the condition is impossible. - Christopher Cormier, Dec 08 2019 Does k exist for every n >= 2? a(7) > 10^7, if it exists. a(7) > 2^64, if it exists. - Giovanni Resta, Dec 01 2019 LINKS Table of n, a(n) for n=2..6. EXAMPLE For n = 6: The base-b expansions of 271 for b = 2..6 are shown in the following table: b | base-b expansion | number of zeros --------------------------------------- 2 | 100001111 | 4 3 | 101001 | 3 4 | 10033 | 2 5 | 2041 | 1 6 | 1131 | 0 PROG (PARI) count_zeros(vec) = #setintersect(vecsort(vec), vector(#vec)) a(n) = for(k=1, oo, for(b=2, n, if(count_zeros(digits(k, b))!=n-b, break, if(b==n, return(k))))) CROSSREFS Sequence in context: A254059 A346551 A180591 * A322951 A156446 A032685 Adjacent sequences: A330080 A330081 A330082 * A330084 A330085 A330086 KEYWORD nonn,base,fini,full AUTHOR Felix Fröhlich, Dec 01 2019 EXTENSIONS Value of a(2) adjusted by Felix Fröhlich, Dec 09 2019 STATUS approved

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Last modified June 3 14:25 EDT 2023. Contains 363116 sequences. (Running on oeis4.)