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Index of Fibonacci Numbers and Variants

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There are many sequences dealing with Fibonacci numbers and n-bonacci numbers. Those related to prime terms are summarized here.

The Fibonacci sequence, 
Fn
, are those numbers defined by the recurrence relation
Fn = Fn − 1 + Fn − 2
and 
F1 = 1
.

See A000045 for an extensive list of references, links, formulas and cross references.

Variants of the Fibonacci numbers utilize a larger set of starting terms and differing initial values.

The offset to these sequences are somewhat arbitrary, most use zero, some use one and others use the first non-zero term.

The table below summarizes sequences in the OEIS related to prime terms of the Fibonacci numbers and variants.

Related Sequences

Column headings in the table below:

order          number of terms summed for next term
seeds          starting value of terms
offset         index of first term
name           name of Fibonacci variant
sequence       A-number of sequence
indices        A-number of sequence listing indices of primes
primes         A-number of sequence listing primes



Sequences
order seeds offset name sequence indices
of primes
primes
2 0,1 0 Fibonacci A000045 A001605 A005478
3 0,0,1 0 Tribonacci A000073 A092835 A092836
3 0,2,1 0 Tribonacci A020992 A233554 A232498
3 1,1,0 0 Tribonacci A081172 A235396 A214752
3 1,1,1 0 Tribonacci A000213 A157611 A056816
3 1,2,2 0 Tribonacci A214727 A234696 A234703
3 1,3,3 0 Tribonacci A214825 A230016 A230017
3 1,4,4 0 Tribonacci A214826 A242315 A242316
3 1,5,5 0 Tribonacci A214827 A242324 A242325
3 1,6,6 0 Tribonacci A214828 A242572 A242576
3 1,7,7 0 Tribonacci A214829 A243622 A243623
3 1,8,8 0 Tribonacci A214830 A244001 A244002
3 1,9,9 0 Tribonacci A214831 A244930 A244931
3 2,1,1 0 Tribonacci A141036 A246517 A246518
3 2,1,2 0 Tribonacci A214899 A233190 A230607
3 2,4,8 0 Tribonacci A135491
3 3,1,1 0 Tribonacci A141523 A235862 A235873
4 0,0,0,1 0 Tetranacci A000078 A104534
4 0,0,1,0 0 Tetranacci A001631 A247027 A247028
4 0,0,1,2 0 Tetranacci A001630 A241660 A241661
4 1,1,1,1 0 Tetranacci A000288 A247561 A247946
5 0,0,0,0,1 0 Pentanacci A001591 A248757 A105757
5 1,1,1,1,1 0 Pentanacci A000322 A248920 A248921
6 0,0,0,0,0,1 0 Hexanacci A001592 A249635 A105759
6 1,1,1,1,1,1 0 Hexanacci A000383 A247192 A249413
7 0,0,0,0,0,0,1 0 Heptanacci A122189 A248700 A105761
7 1,1,1,1,1,1,1 0 Heptanacci A060455 A253318 A253333
8 0,0,0,0,0,0,0,1 0 Octanacci A079262 A253705 A253706
8 1,1,1,1,1,1,1,1 1 Octanacci A123526 A254412 A254413
9 0,0,0,0,0,0,0,0,1 0 Nonanacci A104144 A255529
9 0,0,0,0,0,0,0,1,0 0 Nonanacci A251746 A255530
9 0,0,0,0,0,0,1,0,0 0 Nonanacci A251747 A255531
9 0,0,0,0,0,1,0,0,0 0 Nonanacci A251748
9 0,0,0,0,1,0,0,0,0 0 Nonanacci A251749 A255532
9 0,0,0,1,0,0,0,0,0 0 Nonanacci A251750 A255533
9 0,0,1,0,0,0,0,0,0 0 Nonanacci A251751 A255534
9 0,1,0,0,0,0,0,0,0 0 Nonanacci A251752 A255536
9 1,1,1,1,1,1,1,1,1 1 Nonanacci A127193 A256498 A256499
10 1,1,1,1,1,1,1,1,1,1 1 10-step A127194 A257073 A257074
10 0,0,0,0,0,0,0,0,0,1 0 10-step A122265 A257277 A257278
11 1,1,1,1,1,1,1,1,1,1,1 1 11-step A127624 A257966 A257967

Similar Sequences

Padovan sequence (A000931): start={1,0,0}; offset=0; a(n)=a(n-2)+a(n-3)

Links