A138385 Number of smaller Fibonacci numbers contained in the n-th Fibonacci number in its decimal representation.

0, 0, 0, 0, 0, 0, 0, 2, 2, 1, 1, 1, 1, 2, 1, 2, 1, 2, 3, 2, 1, 2, 1, 3, 2, 3, 5, 2, 3, 3, 4, 5, 6, 4, 4, 2, 5, 4, 4, 4, 8, 5, 2, 2, 4, 5, 4, 6, 4, 3, 5, 5, 6, 4, 4, 6, 5, 4, 5, 4, 6, 6, 6, 7, 7, 4, 6, 8, 6, 3, 6, 7, 5, 6, 8, 6, 6, 6, 5, 8, 6, 6, 7, 6, 5, 4, 6, 6, 5, 4, 5, 6, 8, 7, 6, 5, 6, 7, 8, 10, 6, 6, 7, 7, 6

Offset

0,8

Comments

A138390 and A138391 give record values and where they occur.

Links

Reinhard Zumkeller, Table of n, a(n) for n = 0..10000

Eric Weisstein's World of Mathematics, Fibonacci Number

Example

A000045(40) = 102334155: a(40) = #{0,1,2,3,5,34,55,233} = 8;
A000045(41) = 165580141: a(41) = #{0,1,5,8,55} = 5;
A000045(42) = 267914296: a(42) = #{1,2} = 2;
A000045(43) = 433494437: a(43) = #{3,34} = 2;
A000045(44) = 701408733: a(44) = #{0,1,3,8} = 4;
A000045(45) = 1134903170: a(45) = #{0,1,3,13,34} = 5.

Prog

(Haskell)import Data.List (isInfixOf)
a138385 n = a138385_list !! n
a138385_list = 0 : h [] (map show $ 0 : drop 2 a000045_list) where
   h uss (vs:vss) = length [xs | xs <- uss, xs `isInfixOf` vs] :
                    h (vs : uss) vss
-- Reinhard Zumkeller, Jul 06 2014

Crossrefs

Sequence in context: A030410 A085301 A337565 * A030614 A328615 A128016

Adjacent sequences: A138382 A138383 A138384 * A138386 A138387 A138388

Keyword

nonn,base

Author

Reinhard Zumkeller, Mar 18 2008

Status

approved