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A053029 Numbers with 4 zeros in Fibonacci numbers mod m. 17

%I #15 Feb 22 2022 23:08:22

%S 5,10,13,17,25,26,34,37,50,53,61,65,73,74,85,89,97,106,109,113,122,

%T 125,130,137,146,149,157,169,170,173,178,185,193,194,197,218,221,226,

%U 233,250,257,265,269,274,277,289,293,298,305,313,314,317,325,337,338,346

%N Numbers with 4 zeros in Fibonacci numbers mod m.

%C Conjecture: m is on this list iff m is an odd number all of whose factors are on this list or m is twice such an odd number.

%C A001176(a(n)) = A128924(a(n),1) = 4. - _Reinhard Zumkeller_, Jan 17 2014

%H Reinhard Zumkeller, <a href="/A053029/b053029.txt">Table of n, a(n) for n = 1..1000</a>

%H Brennan Benfield and Michelle Manes, <a href="https://arxiv.org/abs/2202.08986">The Fibonacci Sequence is Normal Base 10</a>, arXiv:2202.08986 [math.NT], 2022.

%H M. Renault, <a href="http://webspace.ship.edu/msrenault/fibonacci/fib.htm">Fibonacci sequence modulo m</a>

%o (Haskell)

%o a053029 n = a053029_list !! (n-1)

%o a053029_list = filter ((== 4) . a001176) [1..]

%o -- _Reinhard Zumkeller_, Jan 17 2014

%Y Cf. A001176.

%Y Cf. A053030 (with 2 zeros), A053031 (with 1 zero).

%K nonn

%O 1,1

%A _Henry Bottomley_, Feb 23 2000

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Last modified May 11 17:45 EDT 2024. Contains 372410 sequences. (Running on oeis4.)