A328733 List of numbers k such that Fibonacci(k) and Fibonacci(k+1) have the same number of prime factors, counted with multiplicity.

1, 3, 4, 8, 9, 15, 27, 37, 38, 44, 68, 104, 116, 124, 170, 201, 202, 205, 214, 291, 302, 361, 381, 387, 403, 428, 469, 474, 502, 507, 514, 565, 584, 602, 603, 622, 628, 663, 668, 669, 675, 698, 710, 745, 763, 766, 865, 872, 873, 898, 922, 968, 1006, 1015, 1018, 1035, 1075, 1146, 1153, 1182

Offset

1,2

Comments

F(1) and F(2), both being 1, count as having zero prime factors each.

0 is not a term since all primes divide 0.

For the corresponding Fibonacci numbers, see A328734.

Links

Table of n, a(n) for n=1..60.

Blair Kelly, Fibonacci factorizations up to 1000 terms

Tomás Roca Sánchez, Python script that uses already factorized numbers of the sequence

Example

F(8) = 21 = 3 * 7, and F(9) = 34 = 2 * 17 have 2 prime factors each, so 8 is a part of the sequence.

Prog

(Python) # See link
(PARI) isok(k) = bigomega(fibonacci(k)) == bigomega(fibonacci(k+1)); \\ Michel Marcus, Nov 11 2019

Crossrefs

Cf. A000045, A038575, A328734.

Sequence in context: A058074 A319875 A123722 * A217788 A273257 A249485

Adjacent sequences: A328730 A328731 A328732 * A328734 A328735 A328736

Keyword

nonn

Author

Tomás Roca Sánchez, Oct 26 2019

Extensions

More terms from Amiram Eldar, Oct 26 2019

Status

approved