A120255 Array read by rows, where the n-th row (of A120256(n) terms) lists the positive divisors, not occurring earlier in the array, of the n-th Fibonacci number.

1, 2, 3, 5, 4, 8, 13, 7, 21, 17, 34, 11, 55, 89, 6, 9, 12, 16, 18, 24, 36, 48, 72, 144, 233, 29, 377, 10, 61, 122, 305, 610, 47, 141, 329, 987, 1597, 19, 38, 68, 76, 136, 152, 323, 646, 1292, 2584, 37, 113, 4181, 15, 33, 41, 123, 165, 205, 451, 615, 1353, 2255, 6765, 26

Offset

2,2

Comments

A permutation of the natural numbers, ordered by A001177 and ties broken by the number itself. Inverse permutation is A119745. - Martin Fuller, Sep 10 2006

Links

Michael De Vlieger, Table of n, a(n) for n = 2..12333 (rows 2 <= n <= 100)

Example

Fibonacci(9) = 34; and the divisors of 34 are 1, 2, 17 and 34. Of these divisors, 1 and 2 occur earlier in the array.
So the 9th row of the array is [17, 34].

Mathematica

f[t_] := Append[t, Select[Divisors[Fibonacci[Length[t] + 1]], FreeQ[Flatten[t], # ] &]]; Flatten@Nest[f, {}, 20] (* Ray Chandler, Jun 14 2006 *)
DeleteDuplicates[Flatten[Divisors[Fibonacci[Range[30]]]]] (* Harvey P. Dale, Apr 13 2020 *)

Crossrefs

Cf. A001177, A119745, A120256.

Sequence in context: A185728 A285492 A272090 * A245608 A244154 A182395

Adjacent sequences: A120252 A120253 A120254 * A120256 A120257 A120258

Keyword

nonn,tabf

Author

Leroy Quet, Jun 13 2006

Extensions

Extended by Ray Chandler, Jun 14 2006

Status

approved