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

Author

Tomás Roca Sánchez, Oct 26 2019

Keywords

• nonn

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.

Examples

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

Links

• Blair Kelly, Fibonacci factorizations up to 1000 terms
• Tomás Roca Sánchez, Python script that uses already factorized numbers of the sequence

Crossrefs

Cf. A000045, A038575, A328734.

Programs

PARI

isok(k) = bigomega(fibonacci(k)) == bigomega(fibonacci(k+1)); \\ Michel Marcus, Nov 11 2019

Python

# See link

Extensions

More terms from Amiram Eldar, Oct 26 2019