Number of set bits in multiple

[kriesel]

Originally Posted by GP2

You are talking about Mersenne primes for which the exponent is itself a Mersenne prime.

http://www.doublemersennes.org

2³−1 (where 3 = 2²−1)
2⁷−1 (where 7 = 2³−1)
2³¹−1 (where 31 = 2⁵−1)
2¹²⁷−1 (where 127 = 2⁷−1)

I was writing about and charting bits fractions for all 50 known Mersenne primes' exponents, of which only a few are themselves Mersenne primes having bits fraction 100% ones, where bits fraction is number of ones in the binary expression divided by number of all bits in the binary expression (suppressing leading zeros).