A099401 Square root of a(n) contains the n-th Fibonacci number as a string of digits to the immediate right of the decimal point (excluding leading zeros).

10, 10, 5, 11, 21, 8, 124, 52, 54, 43, 24, 970, 297, 457, 467, 1520, 2516, 7269, 12414, 3804, 11048, 25020, 135635, 56389, 710228, 44151, 21082, 762684, 696414, 1085414, 6472621, 2979828, 15220551, 72130, 9934617, 79533387

Offset: 1

Author

Gil Broussard, Nov 17 2004

Keywords

• nonn
• base

Examples

			a(1)= 10 because sqrt( 10)= 3.(1)622...
a(2)= 10 because sqrt( 10)= 3.(1)622...
a(3)= 5 because sqrt( 5)= 2.(2)360...
a(4)= 11 because sqrt( 11)= 3.(3)166...
a(5)= 21 because sqrt( 21)= 4.(5)825...
a(6)= 8 because sqrt( 8)= 2.(8)284...
a(7)= 124 because sqrt(124)=11.(13)55...
etc.
		

Crossrefs

Cf. A074841, A074762.

Programs

Mathematica

Do[x = IntegerDigits[Fibonacci[n]]; i = 1; l = {}; While[l != x, d = RealDigits[N[Sqrt[i], 100]]; l = Take[Drop[First[d], Last[d]], Length[x]]; i++ ]; Print[i-1], {n, 1, 36}] (* Ryan Propper, Aug 11 2005 *)

Extensions

Corrected and extended by Ryan Propper, Aug 11 2005