A098100 Write each non-Fibonacci integer >0 on a single label. Put the labels in numerical order to form an infinite sequence L. Now consider the succession of single digits of A000045 (Fibonacci numbers): 1 1 2 3 5 8 1 3 2 1 3 4 5 5 8 9 1 4 4 2 3 3 3 7 7 6 1 0 9... The sequence S gives a rearrangement of the labels that reproduces the same succession of digits, subject to the constraint that the smallest label must be used that does not lead to a contradiction.

11, 23, 58, 132, 134, 558, 9, 14, 4, 2333, 7, 76, 10, 98, 71, 59, 72, 584, 41, 81, 6, 765, 109, 46, 17, 711, 28, 65, 74, 63, 68, 750, 25, 12, 139, 31, 96, 418, 317, 811, 51, 42, 29, 83, 20, 40, 1346, 26, 92, 178, 30, 93, 52, 45, 78, 570, 288, 79, 22, 746, 514, 930, 35

Offset

1,1

Comments

This could be roughly rephrased like this: "Re-write in the most economical way the "Fibonacci pattern" using only non-Fibonacci numbers, but re-arranged. All the numbers of the sequence must be different one from another".

Links

Table of n, a(n) for n=1..63.

Example

We must begin with 1,1,2... and we cannot represent "1" by 1 because this label doesn't exist (available labels carry only non-Fibonacci numbers), so the next possibility is the label "11". For 28657,46368,75025,... we cannot use label "75" in "28 65 74 63 68 75..." since no label begins with a 0. Labels of L cannot be used more than once.

Crossrefs

Sequence in context: A141093 A041236 A097485 * A105967 A097473 A366487

Adjacent sequences: A098097 A098098 A098099 * A098101 A098102 A098103

Keyword

base,easy,nonn

Author

Eric Angelini, Sep 22 2004

Status

approved