Hofstadter-Conway $10,000 sequence: Difference between revisions

=={{header|FutureBasic}==

<lang futurebasic>

include "ConsoleWindow"

// Set width of tab

def tab 9

dim as long Mallows, n, pow2, p2, pPos, uprLim

dim as double p

print

// Adjust array elements depending on size of sequence

_maxArrayElements = 1200000

input "Enter upper limit between 1 and 20 (Enter 20 gives 2^20): "; uprLim

dim as double r

dim as long a( _maxArrayElements )

if uprLim < 1 or uprLim > 20 then uprLim = 20

a(1) = 1

a(2) = 1

pow2 = 2

p2 = 2 ^ pow2

p = 0.5

pPos = 0

print

for n = 3 to 2 ^ uprLim

a(n) = a( a( n-1 ) ) + a( n-a( n-1 ) )

r = a(n) / n

if r >= 0.55 then Mallows = n

if r > p

p = r

pPos = n

end if

if n == p2

print "Maximum of a(n)/n between", " 2^"; pow2-1; " and 2^"; pow2," is "; p;, " at n = "; pPos

pow2 = pow2 + 1

p2 = 2 ^ pow2

p = 0.5

end if

next

print

print "Mallows number is:"; Mallows

</lang>

Output:

<pre>

Enter upper limit between 1 and 20 (Enter 20 gives 2^20): 20

Maximum of a(n)/n between 2^ 1 and 2^ 2 is 0.6666666667 at n = 3

Maximum of a(n)/n between 2^ 2 and 2^ 3 is 0.6666666667 at n = 6

Maximum of a(n)/n between 2^ 3 and 2^ 4 is 0.6363636364 at n = 11

Maximum of a(n)/n between 2^ 4 and 2^ 5 is 0.6086956522 at n = 23

Maximum of a(n)/n between 2^ 5 and 2^ 6 is 0.5909090909 at n = 44

Maximum of a(n)/n between 2^ 6 and 2^ 7 is 0.5760869565 at n = 92

Maximum of a(n)/n between 2^ 7 and 2^ 8 is 0.5674157303 at n = 178

Maximum of a(n)/n between 2^ 8 and 2^ 9 is 0.5594594595 at n = 370

Maximum of a(n)/n between 2^ 9 and 2^ 10 is 0.5549374131 at n = 719

Maximum of a(n)/n between 2^ 10 and 2^ 11 is 0.5501008742 at n = 1487

Maximum of a(n)/n between 2^ 11 and 2^ 12 is 0.5474628926 at n = 2897

Maximum of a(n)/n between 2^ 12 and 2^ 13 is 0.5441447479 at n = 5969

Maximum of a(n)/n between 2^ 13 and 2^ 14 is 0.5424427088 at n = 11651

Maximum of a(n)/n between 2^ 14 and 2^ 15 is 0.5400710975 at n = 22223

Maximum of a(n)/n between 2^ 15 and 2^ 16 is 0.5387840206 at n = 45083

Maximum of a(n)/n between 2^ 16 and 2^ 17 is 0.537043657 at n = 89516

Maximum of a(n)/n between 2^ 17 and 2^ 18 is 0.5360200678 at n = 181385

Maximum of a(n)/n between 2^ 18 and 2^ 19 is 0.5346454311 at n = 353683

Maximum of a(n)/n between 2^ 19 and 2^ 20 is 0.53377923 at n = 722589

Mallows number is: 1489

</pre>