A078609 Least positive integer x such that 2*x^n>(x+3)^n.

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

Offset: 2

Author

Jon Perry, Dec 09 2002

Keywords

• nonn

Examples

			a(2)=8 as 7^2=49, 8^2=64, 10^2=100 and 11^2=121.
		

Crossrefs

Cf. A078607, A078608.

Programs

PARI

for (n=2,50, x=2; while (2*x^n<=((x+3)^n),x++); print1(x","))

Formula

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.

Extensions

Edited by Dean Hickerson, Dec 17 2002