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#936 | |
"Garambois Jean-Luc"
Oct 2011
France
22·3·47 Posts |
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I will probably put the page on my website as shown in post # 925, unless you still make some changes in the layout or in the tags, area where I don't understand much. I will also have less time in the next few days, because unfortunately my vacation is going to end. I can always edit the page later. |
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#937 | |
"Garambois Jean-Luc"
Oct 2011
France
10648 Posts |
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Thank you for this demonstration attempt ! Me, I am focusing on the end of remark 2 of post #921. OK, now the calculations have been done for base 38. But why do we have nothing for bases 6, 12, 24, 30, 72 ...? These are bases which have the factor 3 in their decomposition. But there are others who have the factor 3 and who have something: 18, 42, 882 ... I look at the data over and over again ! |
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#938 | |
"Alexander"
Nov 2008
The Alamo City
22·5·29 Posts |
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![]() PS Regarding above, I did end up finding the formulas, but still couldn't complete the inductive proof. I'll post the formulas here if anyone wants to try their hand at it: Code:
x = ((19^(12*(n+1)+1))-((19^(12*n+1))))/18 y = 2^(12*(n+1)+1)-2^(12*n+1) z = (((19^(12*(n+1)+1))-((19^(12*n+1))))/18) * (2^(12*(n+1))-2) w = (2^(12*(n+1)+1)-2^(12*n+1)) * (((19^((12*n)+1))-19)/18) v = 2^(12*(n+1)) * (((19^(12*(n+1)))-((19^(12*n+1))))/18) prev = 2^(12*n) * 19^(12*n) old = <previous sum> new = old+prev+x+y+z+w+v Last fiddled with by Happy5214 on 2021-03-04 at 12:00 Reason: Adding formulas for 38^12n |
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#939 |
Sep 2008
Kansas
CF516 Posts |
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In keeping with the spirit of investigating base 2*p, next up is base 46.
Preliminary results show a similar phenomena. Additionally, 46^6n shows an abundance of (3 * 5 * 7) along with 46^12n (3 * 5 * 7 * 13) to advance the sequence. |
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#940 | |
Aug 2020
100102 Posts |
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#941 | |
"Garambois Jean-Luc"
Oct 2011
France
22×3×47 Posts |
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Thanks a lot for your help ! I will try to modify the html code like in your example. But I'm running out of time. I think it takes hours of work to rearrange everything like in your example. I hope I am wrong. I don't know when I will be able to publish the page or both pages if I separate the two posts. I will keep you posted... |
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#942 | |
"Garambois Jean-Luc"
Oct 2011
France
22×3×47 Posts |
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OK, seen. Thanks for the base 46. You talk about an abundance of (3 * 5 * 7), didn't you want to write (3^3 * 5 * 7) instead ? |
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#944 |
Sep 2008
Kansas
31·107 Posts |
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#945 | |
Just call me Henry
"David"
Sep 2007
Cambridge (GMT/BST)
10110111000112 Posts |
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#946 |
Just call me Henry
"David"
Sep 2007
Cambridge (GMT/BST)
33×7×31 Posts |
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Assuming no factors below 1e20 then the maximum abundance contribution of the C353 can be upper bounded by ((1e20+1)/1e20)^(floor(353/20))= (1+1e-20)^17= 1.00000000000000000017 or there about.
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Thread Tools | |
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