A097485 Write the positive integers on labels in numerical order, forming an infinite sequence L. Consider now the succession of single digits made by juxtaposing Fibonacci numbers: 1 1 2 3 5 8 1 3 2 1 3 4 5 5 ... (A031324). This sequence gives a derangement of L that produces the same succession of digits, subject to the constraint that the smallest unused label must be used that does not lead to a contradiction.

11, 23, 58, 1, 3, 2, 13, 4, 5, 589, 14, 42, 33, 37, 7, 6, 10, 9, 8, 71, 59, 72, 584, 41, 81, 67, 65, 109, 46, 17, 71, 12, 86, 57, 463, 68, 750, 25, 121, 39, 31, 96, 418, 317, 81, 151, 422, 98, 320

Offset: 1

Author

Eric Angelini, Sep 19 2004

Keywords

• base
• easy
• nonn

Comments

Labels of L can be used only once in this sequence.

We could name this sequence the "Fibo_nat_cci" sequence (nat stands for "natural numbers").

Derangement here means the n-th term of L is not the n-th term of the sequence, so a(n) != n.

Examples

			We must begin with 1,1,2,3,... and we cannot have a(1) = 1, so the next possibility is the label "11". After "68" we must get "7,5,0,2,5,1,2,1,3,9,3,1,9,6,4,1,8..." (corresponding to Fibonacci numbers "75025,121393,196418..."); "7" is already used, and we cannot use "75" since no label begins with a 0. So the next term is "750".
		

Crossrefs

Cf. A000045, A031324, A098067.

Extensions

Derangement wording introduced by Danny Rorabaugh, Nov 27 2015

Initial 0 removed by Danny Rorabaugh, Nov 28 2015