OFFSET
1,2
COMMENTS
The sum of the first n nonzero Fibonacci numbers is F(n+2)-1, sequence A000071. Knott discusses the factorization of these numbers. Most of the terms are divisible by 24. - T. D. Noe, Oct 10 2005, edited by M. F. Hasler, Mar 01 2020
All terms are either multiples of 24 (cf. A124455) or odd (cf. A331976) or congruent to 2 (mod 12), cf. A331870 where this statement is proved. - M. F. Hasler, Mar 01 2020
LINKS
Giovanni Resta, Table of n, a(n) for n = 1..10000 (first 1000 terms from T. D. Noe)
Daniel Yaqubi and Amirali Fatehizadeh, Some results on average of Fibonacci and Lucas sequences, arXiv:2001.11839 [math.CO], 2020.
FORMULA
{n: n| A000071(n+2)}. - R. J. Mathar, Feb 05 2020
EXAMPLE
2 | 4, 24 | 121392, 48 | 12586269024, ... [Corrected by M. F. Hasler, Feb 06 2020]
MAPLE
select(n-> irem(combinat[fibonacci](n+2)-1, n)=0, [$1..3000])[]; # G. C. Greubel, Feb 03 2020
MATHEMATICA
Select[Range[3000], Mod[Fibonacci[ #+2]-1, # ]==0&] (* T. D. Noe, Oct 06 2005 *)
PROG
(PARI) is(n)=((Mod([1, 1; 1, 0], n))^(n+2))[1, 2]==1 \\ Charles R Greathouse IV, Feb 04 2013
(Magma) [1] cat [n: n in [1..3000] | Fibonacci(n+2) mod n eq 1 ]; // G. C. Greubel, Feb 03 2020
(Sage) [n for n in (1..3000) if mod(fibonacci(n+2), n)==1 ] # G. C. Greubel, Feb 03 2020
(GAP) Filtered([1..3000], n-> ((Fibonacci(n+2)-1) mod n)=0 ); # G. C. Greubel, Feb 03 2020
CROSSREFS
KEYWORD
nonn
AUTHOR
Joseph L. Pe, Oct 05 2005
EXTENSIONS
More terms from Rick L. Shepherd and T. D. Noe, Oct 06 2005
STATUS
approved