<body><script type="text/javascript"> function setAttributeOnload(object, attribute, val) { if(window.addEventListener) { window.addEventListener('load', function(){ object[attribute] = val; }, false); } else { window.attachEvent('onload', function(){ object[attribute] = val; }); } } </script> <div id="navbar-iframe-container"></div> <script type="text/javascript" src="https://apis.google.com/js/platform.js"></script> <script type="text/javascript"> gapi.load("gapi.iframes:gapi.iframes.style.bubble", function() { if (gapi.iframes && gapi.iframes.getContext) { gapi.iframes.getContext().openChild({ url: 'https://www.blogger.com/navbar.g?targetBlogID\x3d5974596\x26blogName\x3dWhy?\x26publishMode\x3dPUBLISH_MODE_BLOGSPOT\x26navbarType\x3dBLACK\x26layoutType\x3dCLASSIC\x26searchRoot\x3dhttps://gamindu.blogspot.com/search\x26blogLocale\x3den_US\x26v\x3d2\x26homepageUrl\x3dhttp://gamindu.blogspot.com/\x26vt\x3d8079249296247105828', where: document.getElementById("navbar-iframe-container"), id: "navbar-iframe", messageHandlersFilter: gapi.iframes.CROSS_ORIGIN_IFRAMES_FILTER, messageHandlers: { 'blogger-ping': function() {} } }); } }); </script>
Why?

Why the dickens, not? 

Tuesday, March 08, 2005

The mystery of the ratios

prime(fibb(i)): i=0,1,2.....
sn = 2, 3, 3, 5, 7, 13, 23, 43, 79, 149, 263, 463, 829, 1481, 2593, 4507, 7817, 13477,23167, 39791, 67933,

Ratio:sn+1:sn
1.5,1.0,1.67,1.4,1.87,1.77,1.87,1.84,1.89,1.77,1.79,1.76,1.74,1.72,1.72,1.71

seemingly converges to 1.7

fibb(prime(i)):i=0,1,2........
1, 2, 5, 13, 89, 233, 1597, 4181, 28657, 514229, 1346269, 24157817, 165580141, 433494437

Ratio:sn+1:sn
2,2.5,2.6,6.85,2.62,6.85,2.62,6.85,17.94,2.62,17.94,6.85,2.62

2.62, 6.85, 17.94, make cyclic appearances. credit:sage

can't do a whole lot more with c++ data types, gets buggered in the 47th Fibonacci(long data type issue) and 10,000 oddth prime(static array limit issue). These can be overcome, ofcourse. To continue or not....

<ponders>
update: with my current 500GB machine, i can only go upto i=37(20 so far) for series 1 and i=27(13 so far) for series 2. unless i get a list...

urped by gumz @ 6:01 PM


© gumz 2005 - Powered for Blogger by Blogger Templates

Powered by Blogger Weblog Commenting and Trackback by HaloScan.com