Re: [math-fun] "OneSixOne" palindrome approx to phi
At 01:38 PM 11/23/2015, Henry Baker wrote:
But why stop with 161; cf(phi) is also a palindrome.
Harmony and balance will cost you 2400 euros.
Smaller amounts of harmony and balance are denoted by "Tau" and cost you only 900 euros.
So, for which bases is phi a palindrome for the first 3 digits?
If phi is truncated to 3 base-b digits, I get palindromes for bases b=4, 10, 26, etc.: (the second number is ln(b), so it appears that the sequence is growing logarithmically) b= 4 1.386294361119891 b= 10 2.302585092994046 b= 26 3.258096538021482 b= 68 4.219507705176107 b= 178 5.181783550292085 b= 466 6.144185634125646 b= 1220 7.106606137727303 b= 3194 8.069029328774958 b= 8362 9.03145291191651 b= 21892 9.993876552263808 b= 57314 10.95630020095731
Search for bases in which the first *four* digits make a palindrome? On Mon, Nov 23, 2015 at 9:52 PM, Henry Baker <hbaker1@pipeline.com> wrote:
At 01:38 PM 11/23/2015, Henry Baker wrote:
But why stop with 161; cf(phi) is also a palindrome.
Harmony and balance will cost you 2400 euros.
Smaller amounts of harmony and balance are denoted by "Tau" and cost you only 900 euros.
So, for which bases is phi a palindrome for the first 3 digits?
If phi is truncated to 3 base-b digits, I get palindromes for bases b=4, 10, 26, etc.:
(the second number is ln(b), so it appears that the sequence is growing logarithmically)
b= 4 1.386294361119891 b= 10 2.302585092994046 b= 26 3.258096538021482 b= 68 4.219507705176107 b= 178 5.181783550292085 b= 466 6.144185634125646 b= 1220 7.106606137727303 b= 3194 8.069029328774958 b= 8362 9.03145291191651 b= 21892 9.993876552263808 b= 57314 10.95630020095731
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For b values: http://oeis.org/A052995 , http://oeis.org/A055819 , http://oeis.org/A126358 .
On Nov 23, 2015, at 9:52 PM, Henry Baker <hbaker1@pipeline.com> wrote:
If phi is truncated to 3 base-b digits, I get palindromes for bases b=4, 10, 26, etc.:
Amazing!! Any sufficiently advanced technology is indistinguishable from magic. -- ACClarke At 01:34 AM 11/24/2015, Hans Havermann wrote:
For b values: http://oeis.org/A052995 , http://oeis.org/A055819 , http://oeis.org/A126358 .
On Nov 23, 2015, at 9:52 PM, Henry Baker <hbaker1@pipeline.com> wrote:
If phi is truncated to 3 base-b digits, I get palindromes for bases b=4, 10, 26, etc.:
participants (3)
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Allan Wechsler -
Hans Havermann -
Henry Baker