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A024631
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n written in fractional base 4/3.
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9
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0, 1, 2, 3, 30, 31, 32, 33, 320, 321, 322, 323, 3210, 3211, 3212, 3213, 32100, 32101, 32102, 32103, 32130, 32131, 32132, 32133, 321020, 321021, 321022, 321023, 321310, 321311, 321312, 321313, 3210200, 3210201, 3210202, 3210203, 3210230, 3210231
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OFFSET
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0,3
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LINKS
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FORMULA
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To represent a number in base b, if a digit is greater than or equal to b, subtract b and carry 1. In fractional base a/b, subtract a and carry b.
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MAPLE
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a:= proc(n) `if`(n<1, 0, irem(n, 4, 'q')+a(3*q)*10) end:
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MATHEMATICA
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p:= 4; q:= 3; a[n_]:= a[n]= If[n==0, 0, 10*a[q*Floor[n/p]] + Mod[n, p]]; Table[a[n], {n, 0, 40}] (* G. C. Greubel, Aug 20 2019 *)
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PROG
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(PARI) a(n) = my(p=4, q=3); if(n==0, 0, 10*a(q*(n\p)) + (n%p));
(Sage)
def basepqExpansion(p, q, n):
L, i = [n], 1
while L[i-1] >= p:
x=L[i-1]
L[i-1]=x.mod(p)
L.append(q*(x//p))
i+=1
return Integer(''.join(str(x) for x in reversed(L)))
[basepqExpansion(4, 3, n) for n in [0..40]] # G. C. Greubel, Aug 20 2019
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CROSSREFS
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KEYWORD
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nonn,base,easy
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AUTHOR
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STATUS
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approved
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