Power Floors

Author

Eric W. Weisstein
May 9, 2002

This notebook downloaded from http://mathworld.wolfram.com/notebooks/IntegerSequences/PowerFloors.nb.

For more information, see Eric's MathWorld entry http://mathworld.wolfram.com/PowerFloors.html.

©2005 Wolfram Research, Inc. except for portions noted otherwise

Initialization

<<EISFormat`;

⌊((((3/2)))^n)⌋

Table[Floor[(3/2)^n],{n,20}]

FormatSequence[Drop[Position[PrimeQ[Table[Floor[(3/2)^n],{n,100}]],False]//Flatten,1],
	46037,1,
	Ref->"UPNT E19",
	Name->"n for which (3/2)^n is composite.",
html["Power Floors"]
]

FormatSequence[Select[Rest@Table[Floor[(3/2)^n],{n,100}],!PrimeQ[#]&],
70758 ,1,
Detail->"R. K. Guy, Unsolved Problems in Number Theory, E19",
Name->"Values of Floor[(3/2)^n] that are composite.",
Cross->{43037,70759,70760},
html["Power Floors"]
]

FormatSequence[Drop[Position[PrimeQ[Table[Floor[(3/2)^n],{n,10000}]],True]//Flatten,1],
	070759,1,
Detail->"R. K. Guy, Unsolved Problems in Number Theory, E19",
Name->"n for which Floor[(3/2)^n] is prime.",
Cross->{43037,70758,70760},
html["Power Floors"]
]

FormatSequence[Select[Table[Floor[(3/2)^n],{n,300}],PrimeQ],
70760,1,
Detail->"R. K. Guy, Unsolved Problems in Number Theory, E19",
Name->"Values of Floor[(3/2)^n] that are prime",
Cross->{43037,070758,070759},
html["Power Floors"]
]

⌊((((4/3)))^n)⌋

Table[Floor[(4/3)^n],{n,20}]

FormatSequence[Drop[Position[PrimeQ[Table[Floor[(4/3)^n],{n,100}]],False]//Flatten,2],
	46038,1,
Ref->"UPNT E19",
	Name->"n for which (4/3)^n is composite.",
html["Power Floors"]
]

FormatSequence[Select[Drop[Table[Floor[(4/3)^n],{n,100}],2],!PrimeQ[#]&],
70761 ,1,
Detail->"R. K. Guy, Unsolved Problems in Number Theory, E19",
Name->"Values of Floor[(4/3)^n] that are composite.",
Cross->Sort@{046038,70762,067905},
html["Power Floors"]
]

FormatSequence[Drop[Position[PrimeQ[Table[Floor[(4/3)^n],{n,10000}]],True]//Flatten,1],
	070762,1,
Detail->"R. K. Guy, Unsolved Problems in Number Theory, E19",
Name->"n for which Floor[(4/3)^n] is prime.",
Cross->Sort@{43038,70761,067905},
html["Power Floors"]
]

FormatSequence[Select[Table[Floor[(4/3)^n],{n,600}],PrimeQ],
067905,1,
Detail->"R. K. Guy, Unsolved Problems in Number Theory, E19",
Name->"Values of Floor[(4/3)^n] that are prime",
Cross->Sort@{43038,070761,070762}
]