MaplePrimes - comments on Post, MRB Constant-D

MaplePrimes - comments on Post, MRB Constant-D http://www.mapleprimes.com/posts/37056-MRB-ConstantD en-us 2026 Maplesoft, A Division of Waterloo Maple Inc. Maplesoft Document System Fri, 12 Jun 2026 08:41:58 GMT Fri, 12 Jun 2026 08:41:58 GMT The latest comments added to the Post, MRB Constant-D http://www.mapleprimes.com/images/mapleprimeswhite.jpg MaplePrimes - comments on Post, MRB Constant-D http://www.mapleprimes.com/posts/37056-MRB-ConstantD Attached Worksheet http://www.mapleprimes.com/posts/37056-MRB-ConstantD?ref=Feed:MaplePrimes:MRB Constant-D:Comments#comment64896 I was so excited I forgot to attach the worksheet. Here it is.   <a href="http://mapleoracles.maplesoft.com:8080/maplenet/primes/worksheet/565_near0.mw">View 565_near0.mw on MapleNet</a> or <a href="http://www.mapleprimes.com/files/565_near0.mw">Download 565_near0.mw</a> <a href="http://www.mapleprimes.com/viewfile/3575">View file details</a> The latest comments added to the Post, MRB Constant-D 64896 Fri, 10 Jul 2009 02:52:45 Z Marvin Ray Burns Marvin Ray Burns Use complex numbers for n http://www.mapleprimes.com/posts/37056-MRB-ConstantD?ref=Feed:MaplePrimes:MRB Constant-D:Comments#comment64897 See what happens when you use a domain of complex numbers for n: <a href="http://mapleoracles.maplesoft.com:8080/maplenet/primes/worksheet/565_near0_complex.mw">View 565_near0_complex.mw on MapleNet</a> or <a href="http://beta.mapleprimes.com/files/565_near0_complex.mw">Download 565_near0_complex.mw</a> <a href="http://beta.mapleprimes.com/viewfile/3586">View file details</a> The latest comments added to the Post, MRB Constant-D 64897 Sun, 19 Jul 2009 04:14:03 Z Marvin Ray Burns Marvin Ray Burns Try this oneliner! http://www.mapleprimes.com/posts/37056-MRB-ConstantD?ref=Feed:MaplePrimes:MRB Constant-D:Comments#comment64898 <img src="file:///C:/DOCUME~1/Owner/LOCALS~1/Temp/moz-screenshot-34.jpg" alt="" /><img src="file:///C:/DOCUME%7E1/Owner/LOCALS%7E1/Temp/moz-screenshot-35.jpg" alt="" /><maple></maple> restart; for Digits from 2 to 20 do m := evalf(sum((-1)^i*(i^(1/i)-1), i = 1 .. infinity)); print(evalf(1+sin(5060936308*Pi/m), Digits+5)) end do:restart:   Notice how suddenly the result drops to 10^(-21).     The latest comments added to the Post, MRB Constant-D 64898 Wed, 22 Jul 2009 05:25:26 Z Marvin Ray Burns Marvin Ray Burns Another set of near-integer equations http://www.mapleprimes.com/posts/37056-MRB-ConstantD?ref=Feed:MaplePrimes:MRB Constant-D:Comments#comment64899     Let p be any odd number, as an example, say abs(P)<100, then -sin(996509389*p*Pi/m)  = "+/-1. " .       To see this try       restart; Digits := 62: m := evalf(sum((-1)^i*(i^(1/i)-1), i = 1 .. infinity)):for n from -100 to 100 do p := 2*n-1; printf("%a %a\n", p, evalf(-sin(996509389*p*Pi/m))) end do:       And with half the accuracy,       let p be any even number, as an example, say abs(P)<1000, then -sin(996509389*p*Pi/m) =0.       To see this try       restart; Digits := 62: m := evalf(sum((-1)^i*(i^(1/i)-1), i = 1 .. infinity)):for n from -100 to 100 do p := 2*n; printf("%a %a\n", p, evalf(-sin(996509389*p*Pi/m))) end do:   .   The latest comments added to the Post, MRB Constant-D 64899 Sun, 29 Nov 2009 09:08:33 Z Marvin Ray Burns Marvin Ray Burns Time for a question http://www.mapleprimes.com/posts/37056-MRB-ConstantD?ref=Feed:MaplePrimes:MRB Constant-D:Comments#comment64900   To sum up what I've noticed so far. Concerning the MRB constant, m := evalf(sum((-1)^i*(i^(1/i)-1), i = 1 .. infinity)):     From the first  and fourth posts I have come up the following:   restart; Digits := 22; m := evalf(sum((-1)^i*(i^(1/i)-1), i = 1 .. infinity)); for n from -10 to 10 do p := n; printf("%a %a\n", p, evalf(sin(Pi*(5060936308+78389363*floor(n))/m))) end do   That gives the first set of near-integer equations represented by: -10    -.9999999999999853247439 -9    -.9999999999999881012605 -8   -.9999999999999905882557 -7    -.9999999999999927828150 -6    -.9999999999999946864810 -5    -.9999999999999963001138 -4    -.9999999999999976218224 -3    -.9999999999999986526377 -2    -.9999999999999993929081 -1    -.9999999999999998417661 0    -.9999999999999999997307 1    -.9999999999999998668019 2    -.9999999999999994426460 3    -.9999999999999987277599 4    -.9999999999999977219805 5    -.9999999999999964244621 6    -.9999999999999948367254 7    -.9999999999999929580953 8    -.9999999999999907872146 9    -.9999999999999883266272 10    -.9999999999999855751465   Form the fifth post: <img src="file:///C:/DOCUME%7E1/Owner/LOCALS%7E1/Temp/moz-screenshot-11.png" alt="" />restart; Digits := 22; m := evalf(sum((-1)^i*(i^(1/i)-1), i = 1 .. infinity)); for n from -10 to 10 do p := 2*n-1; printf("%a %a\n", p, evalf(-sin(996509389*p*Pi/m))) end do:   Wich gives the second set: -21    -.9999999999999972039693 -19    .9999999999999977153722 -17    -.9999999999999981691216 -15    .9999999999999985780284 -13   -.9999999999999989307085 -11    .9999999999999992332081 -9    -.9999999999999994855272 -7    .9999999999999996901603 -5    -.9999999999999998417661 -3    .9999999999999999429076 -1    -.9999999999999999936564 1    .9999999999999999936564 3    -.9999999999999999429076 5    .9999999999999998417661 7    -.9999999999999996901603 9    .9999999999999994855272 11    -.9999999999999992332081 13    .9999999999999989307085 15    -.9999999999999985780284 17    .9999999999999981691216 19    -.9999999999999977153722 My question to any one who knows is, aren't these two sets independent?   I mean something like, neither one is true just because the other is, right?   The first involved sin(Pi*(5060936308+78389363*floor(n))/m) The second involved sin(996509389*p*Pi/m) Am I correct in figuring that the periods should be totally unrelated? And has anyone here had any analysis that explains why these two sets exists? And do you think they can help me find a closed form for the MRB constant?             The latest comments added to the Post, MRB Constant-D 64900 Mon, 30 Nov 2009 07:03:31 Z Marvin Ray Burns Marvin Ray Burns Further numeric http://www.mapleprimes.com/posts/37056-MRB-ConstantD?ref=Feed:MaplePrimes:MRB Constant-D:Comments#comment64901  Further numeric investigation shows the coefficients 5060936308, 78389363 and 996509389 can be replaced by 1/2 and 1/3 of their value and still produce remarkable results. <a href="http://beta.mapleprimes.com:8080/maplenet/primes/worksheet/565_MRB_various_fractions.mw">View 565_MRB_various_fractions.mw on MapleNet</a> or <a href="../../../../files/565_MRB_various_fractions.mw">Download 565_MRB_various_fractions.mw</a> <a href="../../../../viewfile/3871">View file details</a> The latest comments added to the Post, MRB Constant-D 64901 Tue, 01 Dec 2009 06:26:23 Z Marvin Ray Burns Marvin Ray Burns