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

• E. S. Croot, [1], Notes on Linear Recurrence Sequences.
• M. A. Lerma, [2], Recurrence Relations.
• Tony D. Noe and Jonathan Vos Post, [3], J. of Integer Sequences, Vol. 8 (2005), Article 05.4.4.
• Weisstein, Eric W., Fibonacci Number, from MathWorld—A Wolfram Web Resource.
• Weisstein, Eric W., Fibonacci n-Step Number, from MathWorld—A Wolfram Web Resource.