A383021 Self-summable Fibonacci numbers: integers k such that Fibonacci(k) divides the sum of the first Fibonacci(k) nonzero Fibonacci numbers.

1, 2, 3, 12, 24, 34, 36, 46, 48, 60, 68, 72, 92, 94, 96, 106, 108, 120, 144, 166, 168, 180, 188, 192, 212, 214, 216, 226, 240, 274, 288, 300, 324, 332, 334, 336, 346, 360, 384, 394, 428, 432, 452, 454, 466, 480, 504, 514, 526, 540, 548, 552, 576, 586, 600, 612

Offset: 1

Author

Oisín Flynn-Connolly, Apr 12 2025

Keywords

• nonn

Comments

Same as integers k such that Fibonacci(k) divides Fibonacci(Fibonacci(k)+2)-1.

Contains infinitely many terms.

Contains all 2p and 4p such that p is prime and p = 2,8 mod 15.

Fibonacci(k) is a subsequence of A124456.

Links

• Amirali Fatehizadeh and Daniel Yaqubi, Average of the Fibonacci numbers, J. Integer Seq. 25 (2022), no. 2, Art. 22.2.6, 10 pp.
• Oisín Flynn-Connolly, On the divisibility of sums of Fibonacci numbers, arXiv:2504.09938 [math.NT], 2025.
• Michal Křížek and Lawrence Somer, Period lengths modulo n and average of terms of second order linear recurrences, Integers 24 (2024), Paper No. A36, 41 pp.

Crossrefs

Cf. A000045, A124456, A158569, A331976, A381053.

Extensions

More terms from Alois P. Heinz, Apr 14 2025