prime(fibb(n)): n=0..59. upperbound:956,722,026,041st prime
sn = 2, 3, 3, 5, 7, 13, 23, 43, 79, 149, 263, 463, 829, 1481, 2593, 4507, 7817, 13477,23167, 39791, 67933, 115837, 196699, 333253, 563999, 951571, 1603493, 2696669, 4528957, 7594787, 12717709, 21275503, 35548199, 59328163, 98921057, 164781997, 274253237, 456074719, 757869829, 1258431703, 2088145753, 3462669647, 5738374573, 9504197513, 15732421259, 26028424949, 43040488583, 71136983143, 117520415707, 194061209371, 320316827161, 528499293521, 871645129727, 1437052096841, 2368368546659, 3901896221693, 6426250163173, 10580359811789, 17414420378039, 28654200525689
ratio:sn+1:sn
1.5, 1, 1.666667, 1.4, 1.857143, 1.769231, 1.869565, 1.837209, 1.886076, 1.765101, 1.760456, 1.790497, 1.78649, 1.750844, 1.738141, 1.734413, 1.724063, 1.719003, 1.717572, 1.707245, 1.705165, 1.698067, 1.694228, 1.692405, 1.687186, 1.685101, 1.681747, 1.679463, 1.676939, 1.674531, 1.672904, 1.670851, 1.66895, 1.667354, 1.665793, 1.66434, 1.662969, 1.661723, 1.660485, 1.659324, 1.658251, 1.657211, 1.656253, 1.655313, 1.654445, 1.653596, 1.652792, 1.65203, 1.651298, 1.650597, 1.649927, 1.649283, 1.648666, 1.648074, 1.647504, 1.646956, 1.646428, 1.64592, 1.64543
Conclusion: ratio gradually decreases from 1.8 - 1.6
fibb(prime(n)): n=0..23 upperbound:fibb(89)=1779979416004714189 at the 64 bit unsigned long limit.
sn = 1, 2, 5, 13, 89, 233, 1597, 4181, 28657, 514229, 1346269, 24157817, 165580141, 433494437, 2971215073, 53316291173, 956722026041, 2504730781961, 44945570212853,308061521170129, 806515533049393, 14472334024676221, 99194853094755497, 1779979416004714189
ratio:sn+1:sn
2, 2.5, 2.6, 6.846154, 2.617978, 6.854077, 2.618034, 6.854102, 17.94427, 2.618034, 17.94427, 6.854103, 2.618034, 6.854102, 17.94427, 17.94427, 2.618034, 17.94427, 6.854102, 2.618034, 17.94427, 6.854102, 17.94427
Conclusion: 2.6, 6.8, 17.9, are the only ratios. these ratios repeat.
my head is broken. inconclusive. programs & methods later. maybe. 128 bit integer arithmetic. maple. mathlab...
urped by gumz @ 2:11 PM
