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A364714
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Least positive integer whose average digit in base b equals (b-1)/2 (the expected value for random digits) for 2 <= b <= n.
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5
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OFFSET
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2,1
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COMMENTS
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a(n) has an even number of digits in all even bases b <= n.
a(8) and a(9) <= 789730327537467540, a(10) <= 789731071815355740, a(11) <= 789731549802436500. - Jason Yuen, May 17 2024
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LINKS
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EXAMPLE
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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.
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PROG
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(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
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CROSSREFS
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KEYWORD
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nonn,base,more,hard
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AUTHOR
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STATUS
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approved
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