A089955 Number of embedded Fibonacci numbers within the n-th Fibonacci number.

0, 0, 0, 0, 0, 0, 2, 2, 1, 2, 1, 1, 3, 1, 1, 1, 2, 3, 3, 1, 1, 3, 3, 2, 3, 7, 3, 5, 4, 3, 5, 5, 5, 4, 3, 5, 5, 4, 4, 10, 7, 3, 4, 4, 7, 7, 7, 3, 2, 7, 5, 6, 8, 6, 9, 9, 7, 7, 5, 8, 6, 8, 7, 8, 6, 8, 10, 8, 3, 7, 10, 6, 10, 8, 9, 6, 8, 7, 12, 11, 9, 11, 7, 8, 11, 7, 11, 10, 6, 9, 8, 9, 13, 11, 7, 13, 14, 11

Offset

1,7

Links

Table of n, a(n) for n=1..98.

Gil Broussard, The Embedded Fibonacci Sequence.

Example

a(26)=7 because Fib(26)=121393 and 7 Fibonacci numbers appear within 121393: 1 appears twice, 3 appears twice and 2, 13 and 21 each appear once.

Mathematica

Table[Total[Table[SequenceCount[IntegerDigits[Fibonacci[n]], IntegerDigits[ Fibonacci[ i]]], {i, 2, n-1}]], {n, 100}] (* The program uses the SequenceCount function from Mathematica version 10 *) (* Harvey P. Dale, Sep 05 2015 *)

Crossrefs

Cf. A000045.

Sequence in context: A182596 A087775 A366091 * A352942 A180312 A178819

Adjacent sequences: A089952 A089953 A089954 * A089956 A089957 A089958

Keyword

nonn,base

Author

Gil Broussard, Jan 12 2004

Status

approved