[seqfan] combination sequence number/Continued frac.loto829 ??

[Don McDonald]

24.05.03   23:52
Dear seqfans,

My 'combination sequence number' uniquely
and easily numbers and counts any
 combinations of 6x lotto numbers in all Lottos.
6/40, 6/49, 6/52 CHOOSE 6 lucky numbers from 1 to 40
 WITHOUT REPLACEMENT.whatever.

It could be applied to an oeis SEQuence that contained
terms e.g.  5 10 15 20 25 30.
(e.g. closest lottery combinations = combination sequence number
has small difference.  rec.gambling.lottery)
Example Below.

Myprog 'SeriCalc4S'  calculates continued fraction convergents.
Example below.

'What is 10-millionth rational in McDonald scheme?' (sci.math)
Simply and uniquely calculates 1-1 map rationals onto natural nos.
Q -> Z+.

don.mcdonald
>  LOTTO.lotoadvice.posts.771.loto829my //loto829nja.s

==============

ENTER 6 LUCKY NUMBERS ascending, LOWEST TO HIGHEST, OR ESCAPE END
?1,4,10,22,25,37
B   A   Z   X
Ball | No. + Ascending | Binomial coeft | Cumulative.
1  1+  1  1
2  4+  3  4
3  10+  84  88
4  22+  5985  6073
5  25+  42504  48577
6  37+  1947792  1996369

Lucky 6 ascending  1, 4, 10, 22, 25, 37, 
(Combination Seqnce Nr#)** = 1996369    (digits 3 6 and 9s.)
nearly 2-millionth combin.

PERCENTILE = 0.52010718 * (40 nCr 6.)

BEGIN, ENTER START NUMBER (Expression),  Q. END
?22,04,10,37,25,01,23,40 lotto.. lucky 6 + 2 bonuses.

(1) 2.20410373E15  DISPLAY COMMA'S (,000)
          2204,103,725,012,340

(2) 2.20410373E15  ƒCTD FRACTION,

( NEEDED TO SWAP SO THAT 0<  A <= B )
 CALCULATE B / A =1E16 / 2.20410373E15
 = 4.53699156  recipr = 0.22041037

CTD-FRAC | NUMERATOR / DENOMIN |=DECIMAL
fraction
............ (pardon, I deleted some.)

6 365  year  xxx/1656= 0.22,04,10,62801932368

1    419/1901= 0.22041031036296685
3    1622/7359= 0.22041038184535944
1    2041/9260= 0.22041036717062634
1    3663  leap year xx /16619= 0.22041037366869246
2    9367/42498= 0.2204103722528119
1    13030/59117= 0.22041037265084493
1    22397/101615= 0.22041037248437731
PREVIOUS LINE IS GOOD APPROXIMATION

5 125015/567192= 0.22041037250172782    **50 cubed.
PREVIOUS LINE IS GOOD APPROXIMATION

6 772487/3504767= 0.22041037250122475     **  11/5. *7/7.
PREVIOUS LINE IS GOOD APPROXIMATION

8 6304911/28605328= 0.22041037250123474
1 7077398/  32110095
     decreasing 3 2..1 0 9.xxx= 0.22041037250123366
very close but not limiting.

1 13382309/60715423= 0.22041037250123416
1 20459707/92825518= 0.22,04,10,37,25,01,23,39.9
PREVIOUS LINE IS GOOD APPROXIMATION better cannot get much better.
lucky 6+2bonus in draw order.


5 115680844/524843013= 0.22041037250123399
1 136140551/617668531= 0.22041037250123399
2 387961946/1.76018008E9= 0.22041037250123399
LIMIT , BIG ENOUGH

...
Q. PROGRAM  SERIcalc4S  E N D.