A109839 Negative numbers written in a bits-of-Pi/primorial base system.

1, 10, 11, 20, 21, 16400, 16401, 16410, 16411, 16420, 16421, 16300, 16301, 16310, 16311, 16320, 16321, 16200, 16201, 16210, 16211, 16220, 16221, 16100, 16101, 16110, 16111, 16120, 16121, 16000, 16001, 16010, 16011, 16020, 16021, 15400

Offset: 1

Author

Rick L. Shepherd, Jul 05 2005

Keywords

• base
• nonn

Comments

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

Examples

			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.
		

References

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

Crossrefs

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