

A244041


Sum of digits of n written in fractional base 4/3.


9



0, 1, 2, 3, 3, 4, 5, 6, 5, 6, 7, 8, 6, 7, 8, 9, 6, 7, 8, 9, 9, 10, 11, 12, 8, 9, 10, 11, 10, 11, 12, 13, 8, 9, 10, 11, 11, 12, 13, 14, 12, 13, 14, 15, 9, 10, 11, 12, 11, 12, 13, 14, 14, 15, 16, 17, 14, 15, 16, 17, 10, 11, 12, 13, 11, 12, 13, 14, 14, 15, 16, 17
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OFFSET

0,3


COMMENTS

The base 4/3 expansion is unique and thus the sum of digits function is welldefined.


LINKS



FORMULA

a(n) < 3 log(n)/log(4/3) < 11 log(n) for n > 1. Possibly the constant factor can be replaced by 7 or 8.  Charles R Greathouse IV, Sep 22 2022


EXAMPLE

In base 4/3 the number 14 is represented by 3212 and so a(14) = 3 + 2 + 1 + 2 = 8.


MATHEMATICA

p:=4; q:=3; a[n_]:= a[n]= If[n==0, 0, a[q*Floor[n/p]] + Mod[n, p]]; Table[a[n], {n, 0, 75}] (* G. C. Greubel, Aug 20 2019 *)


PROG

(Sage)
def base43sum(n):
L, i = [n], 1
while L[i1]>3:
x=L[i1]
L[i1]=x.mod(4)
L.append(3*floor(x/4))
i+=1
return sum(L)
[base43sum(n) for n in [0..75]]
(PARI) a(n) = p=4; q=3; if(n==0, 0, a(q*(n\p)) + (n%p));


CROSSREFS



KEYWORD

nonn,base


AUTHOR



STATUS

approved



