[math-fun] Fraction of indivisible numbers
From: "Schroeppel, Richard" <rschroe@sandia.gov>
product (1 - z^n) for z = 1/2.
1 - 2^-1 - 2^-2 + 2^-5 + 2^-7 - ...
The exponents are (negative) pentagonal numbers. The binary expansion of .2887... should be interesting.
Starting after the radix point, 1 zero, 1 one, 2 zeroes, 1 one, 2 zeroes, 4 ones, 1 zero, 3 ones, 6 zeroes, 1 one, 4 zeroes, 8 ones, 1 zero, 5 ones, 10 zeroes, 1 one, 6 zeroes, 12 ones, ... --Steve
----- Original Message ----- From: "Steve Witham" <sw@tiac.net> To: <math-fun@mailman.xmission.com> Sent: Thursday, April 03, 2008 3:31 PM Subject: [math-fun] Fraction of indivisible numbers
From: "Schroeppel, Richard" <rschroe@sandia.gov>
product (1 - z^n) for z = 1/2.
1 - 2^-1 - 2^-2 + 2^-5 + 2^-7 - ...
The exponents are (negative) pentagonal numbers. The binary expansion of .2887... should be interesting.
This is somehow related to the partition number gf, right? Is there any connection back to the original problem?
participants (2)
-
David Wilson -
Steve Witham