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Search: id:A078609
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| A078609 |
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Least positive integer x such that 2*x^n>(x+3)^n. |
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+0
3
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| 8, 12, 16, 21, 25, 29, 34, 38, 42, 47, 51, 55, 60, 64, 68, 73, 77, 81, 86, 90, 94, 99, 103, 107, 112, 116, 120, 125, 129, 133, 138, 142, 146, 150, 155, 159, 163, 168, 172, 176, 181, 185, 189, 194, 198, 202, 207, 211, 215, 220, 224, 228, 233, 237, 241, 246, 250
(list; graph; listen)
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OFFSET
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2,1
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FORMULA
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a(n) = ceiling(3/(2^(1/n)-1)). For most n, a(n) = floor(3n/log(2)-1/2), but there are exceptions, starting with n=32 and n=52113.
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EXAMPLE
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a(2)=8 as 7^2=49, 8^2=64, 10^2=100 and 11^2=121.
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PROGRAM
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(PARI) for (n=2, 50, x=2; while (2*x^n<=((x+3)^n), x++); print1(x", "))
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CROSSREFS
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Cf. A078607, A078608.
Sequence in context: A063539 A081925 A049199 this_sequence A084809 A110558 A036705
Adjacent sequences: A078606 A078607 A078608 this_sequence A078610 A078611 A078612
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KEYWORD
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nonn
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AUTHOR
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Jon Perry (perry(AT)globalnet.co.uk), Dec 09 2002
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EXTENSIONS
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Edited by Dean Hickerson (dean(AT)math.ucdavis.edu), Dec 17 2002
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