A105150 Approximation to leading digit of n-th Fibonacci number.

0, 1, 1, 2, 3, 5, 8, 1, 2, 3, 5, 8, 1, 2, 3, 5, 8, 1, 2, 3, 5, 8, 1, 2, 3, 5, 8, 1, 2, 3, 5, 8, 1, 2, 3, 5, 8, 1, 2, 3, 5, 8, 1, 2, 3, 5, 8, 1, 2, 3, 5, 8, 1, 2, 3, 5, 8, 1, 2, 3, 5, 8, 1, 2, 3, 5, 8, 1, 2, 3, 5, 8, 1, 2, 3, 5, 8, 1, 2, 3, 5, 8, 1, 2, 3, 5, 8, 1, 2, 3, 5, 8, 1, 2, 3, 5, 8, 1, 2, 3, 5, 8, 1, 2, 3

Offset

0,4

Comments

a(0) = 1, a(1) = a(2) = 1 and for n > 2:

a(n) = floor(w/10) + (w mod 10)*0^floor(w/10) where

w = (x+y)*0^(z-1) + y + z*0^floor((11-z)/10),

x = a(n-3), y = a(n-2) and z = a(n-1);

a(n) = A008963(n) = A000030(A000045(n) for n<=14.

Links

Table of n, a(n) for n=0..104.

Example

n=11, x=2, y=3, z=5: w = (2+3) * 0^(5-1)+3+5*0^[(11-5)/10] = 5*0^4+3+5*0^0 = 0+3+5*1 = 8, a(11) = [8/10] + (8 mod 10) * 0^[8/10] = 0 + 8*0^0 = 8;
n=12, x=3, y=5, z=8: w = (3+5) * 0^(8-1)+5+8*0^[(11-8)/10] = 8*0^7+5+8*0^0 = 0+5+8*1 = 13, a(12) = [13/10] + (13 mod 10) * 0^[13/10] = 1 + 3*0^1 = 1;
n=13, x=5, y=8, z=1: w = (5+8) * 0^(1-1)+8+1*0^[(11-1)/10] = 13*0^0+8+1*0^1 = 13*1+8+1*0 = 21, a(13) = [21/10] + (21 mod 10) * 0^[21/10] = 2 + 1*0^2 = 2.

Crossrefs

Sequence in context: A136740 A105994 A120496 * A008963 A031324 A226251

Adjacent sequences: A105147 A105148 A105149 * A105151 A105152 A105153

Keyword

nonn,base

Author

Reinhard Zumkeller, Apr 10 2005

Status

approved