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 A111035 Numbers n that divide the sum of the first n nonzero Fibonacci numbers. 11
 1, 2, 24, 48, 72, 77, 96, 120, 144, 192, 216, 240, 288, 319, 323, 336, 360, 384, 432, 480, 576, 600, 648, 672, 720, 768, 864, 960, 1008, 1080, 1104, 1152, 1200, 1224, 1296, 1320, 1344, 1368, 1440, 1517, 1536, 1680, 1728, 1800, 1920, 1944, 2016, 2064, 2160 (list; graph; refs; listen; history; text; internal format)
 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 See A101907 for another version. Cf. A111058 (the analog for Lucas numbers). Cf. A124455 (k for a(n) = 24k), A124456 (other a(n)), A331976 (odd a(n)), A331870 (even a(n) != 24k). Sequence in context: A119070 A181283 A073215 * A349188 A249277 A002552 Adjacent sequences: A111032 A111033 A111034 * A111036 A111037 A111038 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

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Last modified March 29 15:24 EDT 2023. Contains 361599 sequences. (Running on oeis4.)