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b[n]q
: rebase from base b into base q
In 2005, Marc LeBrun described the rebasing notation (cf. A000695):
 This may be described concisely using the "rebase" notation
b[n]q
, which means "replace b with q in the expansion of n", thus rebasing" n from base b into base q. The present sequence is2[n]4
. Many interesting operations (e.g.,10[n](1/10)
= digit reverse, shifted) are nicely expressible this way.
 Note that
q[n]b
is (roughly) inverse tob[n]q
.
 It's also natural to generalize the idea of "basis" so as to cover the likes of
F[n]2
, the socalled "fibbinary" numbers (A003714) nd provide standard readymade images of entities obeying other arithmetics, say likeGF2[n]2
(e.g., primes = A014580, squares = the present sequence, etc.).
The following table shows relevant pertinent sequences in the OEIS:
b=2  b=3  b=4  b=5  b=6  b=7  b=8  b=9  b=10  

q=2  A065361  A065362^{2}  A215088  A215089  A203580  A028897  
q=3  A005836^{1}  A215090  A215092^{2}  A028898  
q=4  A000695  A023717  A303787  A028899  
q=5  A033042  A037453^{2}  A037459^{2}  A303788  A028900  
q=6  A033043  A037454  A037460  A037465  A303789  A028901  
q=7  A033044^{1}  A037455  A037461^{2}  A037466  A037470  A028902  
q=8  A033045  A037456  A037462  A037467  A037471  A037474  A028903  
q=9  A033046  A037463  A037468  A037472  A037475  A037477  A028904  
q=10  A007088  A007089  A007090  A007091  A007092  A007093  A007094  A007095 A037479^{2} 

q=11  A033047  
q=12  A033048  A102487^{1}  
q=13  A033049  A094823  
q=14  A033050  
q=15  A033051  
q=16  A033052  A102489  
q=17  A197351  
q=18  A197352  
q=19  A197353  
q=20  A063012  A102491^{1} 
^{1} These sequences have offset 1 and start with n=0.
^{2} These sequences have offset 1 and start with n=1.
All other sequences have offset 0 and start with n=0.
Sums of distinct powers of q
The first column (b=2) of the table above shows the sequences for Sums of distinct powers of q, since the binary digits in n enumerate all such powers.
Examples
A037454: 3[n]6 n = 0 1 2 3 4 5 6 7 8 9 10 11 a(n) = 0, 1, 2, 6, 7, 8, 12, 13, 14, 36, 37, 38, ... n = 11: 11_{10} = 102_{3} > 102_{6} = 1*6^2 + 0*6^1 + 2*6^0 = 38_{10} = a(11)
Programs
 (Mathematica)
b:=3; q:=6; Table[FromDigits[RealDigits[n, b], q], {n, 0, 100}]
 (PARI)
b=3; q=6; for(n=0,100,print1(fromdigits(digits(n, b), q),","));
 Java (jOEIS)
java cp joeis.jar irvine.oeis.a037.A037454 3 6