AXIOM SESSIONscale=2.5]
FermatNumber(n:PositiveInteger):PositiveInteger == 2**2**n + 1
Type: Void
Time: 0 sec
l := [FermatNumber(i) for i in 1..6]
(2) [5,17,257,65537,4294967297,18446744073709551617]
Type: List PositiveInteger
Time: 0.01 (IN) + 0.01 (OT) = 0.02 sec
[prime?(n) for n in l]
(3) [true,true,true,true,false,false]
Type: List Boolean
Time: 0.01 (EV) + 0.02 (OT) = 0.03 sec
[factor(n) for n in l]
(4) [5,17,257,65537,641 6700417,274177 67280421310721]
Type: List Factored Integer
Time: 0.04 (EV) + 0.01 (OT) = 0.05 sec
-- factor FermatNumber(7)
[factorial(n) for n in 99..101]
(5)
[
93326215443944152681699238856266700490715968264381621468592963895217599993_
2299156089414639761565182862536979208272237582511852109168640000000000000_
000000000
,
93326215443944152681699238856266700490715968264381621468592963895217599993_
2299156089414639761565182862536979208272237582511852109168640000000000000_
00000000000
,
94259477598383594208516231244829367495623127947025437683278893534169775993_
1622147650308786159180834691162349000354959958336970630260326400000000000_
0000000000000
]
Type: List Integer
Time: 0.01 (EV) + 0.01 (OT) = 0.02 sec
S(n:PositiveInteger):Fraction Integer == reduce(+,[1/k**2 for k in 1..n])
Type: Void
Time: 0 sec
[S(n) for n in 1..20]
(7)
5 49 205 5269 5369 266681 1077749 9778141 1968329 239437889
[1, -, --, ---, ----, ----, ------, -------, -------, -------, ---------,
4 36 144 3600 3600 176400 705600 6350400 1270080 153679680
240505109 40799043101 40931552621 205234915681 822968714749
---------, -----------, -----------, ------------, ------------,
153679680 25971865920 25971865920 129859329600 519437318400
238357395880861 238820721143261 86364397717734821 17299975731542641
---------------, ---------------, -----------------, -----------------]
150117385017600 150117385017600 54192375991353600 10838475198270720
Type: List Fraction Integer
Time: 0.03 (OT) = 0.03 sec