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ROSECODE 252

Complex Base 1

Philippe_57721 · Math ·

A complex integer is a number p+q×i(i2=1) where p and q are integers.

It can be proved that every complex integer has a unique representation in base i1 with 'digits' 0 or 1.

For instance, we have:
2=0×(1+i)0+0×(1+i)1+1×(1+i)2+1×(1+i)3//1100 6=0×(1+i)0+0×(1+i)1+1×(1+i)2+1×(1+i)3+1×(1+i)4+ +0×(1+i)5+1×(1+i)6+1×(1+i)7+1×(1+i)8//111011100

Actually, 6 is the smallest natural integer whose representation contains 6 digits to '1'

Let's define the function R(n) for an natural integer n as follow: consider the digits of n in base i1 as the binary representation of an integer.
Thus:
R(2) = 12
R(6) = 476

Find the smallest integer a, whose representation contains 60 digits
Find the smallest integer b, whose representation contains 93 digits to '1'

Answer format: a,R(a),b,R(b)

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