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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.)