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 A364714 Least positive integer whose average digit in base b equals (b-1)/2 (the expected value for random digits) for 2 <= b <= n. 5
 2, 38, 141, 3468, 36990, 36990 (list; graph; refs; listen; history; text; internal format)
 OFFSET 2,1 COMMENTS a(n) has an even number of digits in all even bases b <= n. a(8) > 6*10^11. a(8) <= 795482814912042180, a(9) and a(10) <= 836119295625913740. - Giorgos Kalogeropoulos, Aug 09 2023 LINKS Table of n, a(n) for n=2..7. EXAMPLE For n = 4, 141 is 10001101 in binary with average digit 1/2, 12020 in base 3 with average digit 2/2 = 1, and 2031 in base 4 with average digit 3/2. No smaller number has this property, so a(4) = 141. PROG (PARI) isokb(k, b) = my(d=digits(k, b)); vecsum(d)/#d == (b-1)/2; isok(k, n) = for (b=2, n, if (!isokb(k, b), return(0)); ); 1; a(n) = my(k=1); while (!isok(k, n), k++); k; \\ Michel Marcus, Aug 05 2023 CROSSREFS a(2)-a(7) are the first terms of A031443, A144798, A144799, A144800, A144801, and A144812, respectively. Sequence in context: A075459 A050248 A337773 * A105645 A098456 A214909 Adjacent sequences: A364711 A364712 A364713 * A364715 A364716 A364717 KEYWORD nonn,base,more,hard AUTHOR Pontus von Brömssen, Aug 04 2023 STATUS approved

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Last modified March 1 05:26 EST 2024. Contains 370430 sequences. (Running on oeis4.)