You can calculate phi to arbitrary precision in J. [Mailer may break long lines below.]
NB. From J Phrases sqrt=:4 : '-:@(+y.&%)^:(>.2^.1>.x.-16) x:%:y.' NB. phi y gives phi correct to y digits phi=:13 : '-:>: y. sqrt 5' NB. Following copied from reference phibook=:'1.61803398874989484820458683436563811772030917980576286213544862270526046281890' phij=:0j77": phi 78 phij 1.61803398874989484820458683436563811772030917980576286213544862270526046281890 phibook 1.61803398874989484820458683436563811772030917980576286213544862270526046281890 Best wishes, John p j wrote: > Bill, > thanks I guess... using phi seems to get the "right" > answers for first few digits of k up to 100000 not 76, > but I can see how that would explain it breaking for > high k. Using phi of 80 digits or so (first row from > page below), made my formula accurate enough to get > right numbers for k>300000 > > http://www.worldwideschool.org/library/books/sci/math/MiscellaneousMathematicalConstants/chap46.html > > Roger, > > It was easy to miss but the results produce useful > notation after you set the global print precision to > > 9!:11 (15) > >>> > I can not relate your statement > > the above formula produces the first few digits of > the > kth fibonacci number. > > with the following result: > > fibfirst i.4 5 > 4.47214e10 7.23607e10 1.17082e10 1.89443e10 3.06525e10 > > ---- > > > fibfirst=: 3 : 0 > p=. 1.61803398874991595753 NB. -: >: ( %: 5) > a =. ((y.) * (10^. p)) - 10^.2.2360679774997898 > a =. 10 + a - (<. a) > 10^a > ) > > the above formula produces the first few digits of the > kth fibonacci number. > > the following list are offsets from 300000 that > produce fibonacci numbers with digits 1-9 pandigital. > (302079, 303585 etc...) > 2079 3585 4120 4651 5079 9027 12850 16912 22309 22658 > 22723 24531 32770 33578 33851 34494 35588 36987 38128 > 41512 43091 43387 51186 57068 57512 59737 59766 70611 > 71824 83432 95911 97945 > > according to this site, > http://www.mcs.surrey.ac.uk/Personal/R.Knott/Fibonacci/fibFormula.html#LOG > > Most of these numbers are actually not pandigital. > My formula is higher by 1-4 on the first 9 digits. Is > this because I have chosen different precision for > phi? > If so, this would be weird because my phi number (p) > is smaller than the rounding choices at that web site > (so I would expect my numbers would be smaller). > > Is there some internal rounding in J that could create > the discrepency? > > > > > > > __________________________________________________________ > Find your next car at http://autos.yahoo.ca > ---------------------------------------------------------------------- > For information about J forums see http://www.jsoftware.com/forums.htm > ---------------------------------------------------------------------- For information about J forums see http://www.jsoftware.com/forums.htm
