Simon: Try series( ( (1/x)^128+1)^(1/4),x=0,500); on Maple. Your binary expansion comes, for example, from the case x= 1/2. I think this goes a long way to explaining the pattern you are seeing. On 3/18/14, 11:34 AM, Simon Plouffe wrote:
... but that number 1 + 2^(1 - 2^13), in base 2 is just 1 position, no ?
the simplest case like sqrt(sqrt(2^n+1)), has a pattern that I can't explain, well, so far, what rule is it ??? (in cellular automatas).
here is a capture of the middle part
00000000000000000000011111111111111111111111 11111111111111111111111111111111111111111111 00000000000000000000000000000000000000000000 00000000000000000001101111111111111111111111 11111111111111111111111111111111111111111111 00000000000000000000000000000000000000000000 00000000000000001110011011111111111111111111 11111111111111111111111111111111111111111111 00000000000000000000000000000000000000000000 00000000000010010110001101111111111111111111 11111111111111111111111111111111111111111111 00000000000000000000000000000000000000000000 00000000011011010010010010101111111111111111 11111111111111111111111111111111111111111111 00000000000000000000000000000000000000000000 00000101010010100101111010000111111111111111 11111111111111111111111111111111111111111111 00000000000000000000000000000000000000000000 01000100100010100000011100000101111111111111 11111111111111111111111111111111111111111111 00000000000000000000000000000000000000000000 10010011011111001100101110000110111111111111 11111111111111111111111111111111111111111111 00000000000000000000000000000000000000000000 11011110100010100101000111111111001011111111
not simple but : always the same. there should be a formula for this !
Best regards, Simon Plouffe
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