[seqfan] Relations between odious and evil numbers

Vladimir Shevelev shevelev at bgu.ac.il
Wed Jan 18 14:49:33 CET 2012

Dear Seqfans,

I submitted to OEIS , in my opinion,  interesting relations connecting  the odious (A000069) and evil (A001969) numbers. They are contained in the following general formula:
For every real x, we have
For example, for k=2, 1^2+2^2+4^2+7^2=0^2+3^2+5^2+6^2=70; 1.2^2+2.2^2+4.2^2+7.2^2=0.2^2+3.2^2+5.2^2+6.2^2=75.76.
I proved them in 1997 in a provincial journal in Russia and think that they till now were unknown.


 Shevelev Vladimir‎

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