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Negative numbers written in a bits-of-Pi/primorial base system.
1

%I #3 Mar 30 2012 17:36:43

%S 1,10,11,20,21,16400,16401,16410,16411,16420,16421,16300,16301,16310,

%T 16311,16320,16321,16200,16201,16210,16211,16220,16221,16100,16101,

%U 16110,16111,16120,16121,16000,16001,16010,16011,16020,16021,15400

%N Negative numbers written in a bits-of-Pi/primorial base system.

%C A109838 describes this representation system which is my example of a type appearing in one of Long's exercises.

%D Calvin T. Long, Elementary Introduction to Number Theory, 2nd ed., D.C. Heath and Company, 1972, p. 30.

%e a(6) = 16400 because -6 = -210 + 180 + 24 = ((-1)^1)*1*210 + ((-1)^0)*6*30 + ((-1)^0)*4*6 + ((-1)^1)*0*2 + ((-1)^1)*0*1, where 1,1,0,0,1 are the first five terms of A004601 and 1,2,6,30,210 are the first five terms of A002110.

%Y Cf. A109838 (nonnegative integers represented similarly), A004601 (Pi in binary), A002110 (primorials), A049345 (primorial base).

%K base,nonn

%O 1,2

%A _Rick L. Shepherd_, Jul 05 2005