[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
sum{i=1,...,2^k}(A000069(i)+x)^k=sum{i=1,...,2^k}(A001969(i)+x)^k.
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.
Regards,
Vladimir
Shevelev Vladimir
More information about the SeqFan
mailing list