A192543 Let r be the largest real zero of x^n - x^(n-1) - x^(n-2) - ... - 1 = 0. Then a(n) is the value of k which satisfies the equation 0.5/10^k < 2 - r < 5/10^k.

0, 1, 1, 1, 2, 2, 2, 3, 3, 3, 4, 4, 4, 4, 5, 5, 5, 6, 6, 6, 7, 7, 7, 7, 8, 8, 8, 9, 9, 9, 10, 10, 10, 10, 11, 11, 11, 12, 12, 12, 13, 13, 13, 13, 14, 14, 14, 15, 15, 15, 16, 16, 16, 16, 17, 17, 17, 18, 18, 18, 19, 19, 19, 19, 20, 20, 20, 21, 21, 21, 22, 22, 22

Offset: 1

Author

Ruskin Harding, Dec 31 2012

Keywords

• base
• nonn

Comments

Same as A034887 except for the offset and a(1). - T. D. Noe, Feb 11 2013

Examples

			For n = 5, the root is approximately r = 1.96594823. The value of k that satisfies 0.5/10^k < 2-r < 5/10^k is 2 as 0.005 < 0.03405177 < 0.05. So a(5) = 2.
		

Links

• Charles R Greathouse IV, Table of n, a(n) for n = 1..10000

Programs

PARI

a(n)=if(n>1, -log(4-2*solve(x=1.5,2,x^n-(1-x^n)/(1-x)))\log(10)+1, 0) \\ Charles R Greathouse IV, Jan 15 2013