Every even perfect number is of the form a(n) + 1 for some n.
Sent: Wednesday, December 31, 2014 at 4:49 AM From: "Stuart Anderson" <stuart.errol.anderson@gmail.com> To: math-fun@mailman.xmission.com Subject: [math-fun] 2015 -> 11111011111 (binary)
The most interesting property of the number 2015 that I could find is that in binary it is the palindromic string with a single zero 11111011111. Considering such palindromic numbers starting from 101, 11011, 1110111, 111101111, 11111011111 gives integers 5, 27, 119, 495, 2015, 8127, 32639, 130815, 523775, 2096127, 33550335, .... Using the formula a(n)= 2^(2n+1) - 2^n - 1 So the next time this happens is in 8127.
This would be a nice opportunity for the NYE firework operators on the Sydney Harbour Bridge to display 2015 in binary - 5 large jets on each side, along with a circular firework from the center of the arch.
Stuart _______________________________________________ math-fun mailing list math-fun@mailman.xmission.com https://mailman.xmission.com/cgi-bin/mailman/listinfo/math-fun