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 A254596 Convert number n to each of the bases from 2 to 10. a(n) is the minimum base that maximizes the sum of digits. 3
 2, 3, 4, 5, 6, 7, 8, 9, 10, 6, 6, 7, 7, 8, 8, 9, 9, 10, 10, 7, 8, 8, 8, 5, 9, 9, 7, 10, 10, 8, 8, 7, 7, 7, 9, 10, 10, 10, 10, 7, 7, 9, 9, 9, 8, 8, 8, 7, 10, 9, 9, 9, 9, 8, 8, 10, 10, 10, 10, 9, 9, 9, 8, 10, 10, 10, 10, 10, 10, 9, 9, 10, 10, 10, 10, 10, 10, 10 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,1 COMMENTS For n <= 10^6 the frequencies are: 2 ->        1 (highest number: 1) 3 ->        1 (highest number: 2) 4 ->        7 (highest number: 832123) 5 ->     8607 (highest number: 993124) 6 ->    29338 (highest number: 995105) 7 ->   110167 (highest number: 991612) 8 ->   153583 (highest number: 999423) 9 ->   251998 (highest number: 1000000) 10 ->  446298 (highest number: 999999) 2 only occurs at a(1) and 3 only occurs at a(2), but all the other numbers, 4 through 10, occur with increasing frequency. 4 occurs at n: 3, 730, 731, 631530, 631531, 832122, 832123, ..., . - Robert G. Wilson v, Feb 05 2015 From Robert G. Wilson v, Feb 11 2015: (Start) The following table is a count of the frequencies of the bases, b, 2 through 10, and for exponents, e, 1 through 9, of 10: \b..2..3...4........5.........6.........7..........8..........9.........10 e\ 1   1  1   1        1         2         1          1          1          1 2   1  1   1        2         4        15         14         19         43 3   1  1   3       19        61       127        171        233        384 4   1  1   3      161       419      1152       1525       2445       4293 5   1  1   3     1168      3706     12152      16503      24138      42328 6   1  1   7     8607     29338    110167     153583     251998     446298 7   1  1   7    66461    313656    918927    1559502    2616635    4524810 8   1  1  11   421478   2262670   8075616   16460917   25832934   46946372 9   1  1  26  3910736  19645806  77440365  167615009  254855326  476532730 (End) LINKS Paolo P. Lava, Table of n, a(n) for n = 1..1000 EXAMPLE 11 in base 2 is 1011 -> sum of digits: 3; 11 in base 3 is 102 -> sum of digits: 3; 11 in base 4 is 23 -> sum of digits: 5; 11 in base 5 is 21 -> sum of digits: 3; 11 in base 6 is 15 -> sum of digits: 6; 11 in base 7 is 14 -> sum of digits: 5; 11 in base 8 is 13 -> sum of digits: 4; 11 in base 9 is 12 -> sum of digits: 3; 11 in base 10 is 11 -> sum of digits: 2. Therefore a(11) = 6. MAPLE with(numtheory): P:=proc(q) local a, b, c, d, j, k, n; for n from 1 to q do c:=0; for k from 2 to 10 do a:=convert(n, base, k); b:=add(a[j], j=1..nops(a)); if b>c then c:=b; d:=k; fi; od; print(d); od; end: P(10^4); MATHEMATICA f[n_] := Block[{a = Plus @@@ IntegerDigits[ n, {2, 3, 4, 5, 6, 7, 8, 9, 10}]}, 1 + Position[a, Max@ a][[1, 1]]]; Array[f, 79] (* Robert G. Wilson v, Feb 04 2015 *) CROSSREFS Cf. A254597. Sequence in context: A292267 A305810 A171060 * A286603 A291751 A275987 Adjacent sequences:  A254593 A254594 A254595 * A254597 A254598 A254599 KEYWORD nonn,base AUTHOR Paolo P. Lava, Feb 02 2015 STATUS approved

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Last modified February 20 17:04 EST 2020. Contains 332080 sequences. (Running on oeis4.)