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A100992 Indices k of Fibonacci numbers F(k) (A000045) that are divisible by k+1. 3

%I #17 Mar 30 2021 08:48:00

%S 10,18,28,30,40,58,60,70,78,88,100,108,130,138,148,150,178,180,190,

%T 198,210,228,238,240,250,268,270,280,310,330,348,358,378,388,400,408,

%U 418,420,430,438,441,448,460,478,490,498,508,520,540,568,570,598,600,618

%N Indices k of Fibonacci numbers F(k) (A000045) that are divisible by k+1.

%C When k+1 is prime, it is in A045468; when k+1 is composite (such as 442), it is in A069106. - _T. D. Noe_, Dec 13 2004

%H Amiram Eldar, <a href="/A100992/b100992.txt">Table of n, a(n) for n = 1..10000</a>

%H Ron Knott, <a href="http://www.maths.surrey.ac.uk/hosted-sites/R.Knott/Fibonacci/fibmaths.html">Mathematical Magic of the Fibonacci Numbers</a>.

%e 18 is a term because F(18) = 2584 = 2*2*2*17*19 is divisible by 19, one more than its index number 18.

%t Select[ Range[ 620], Mod[ Fibonacci[ # ], # + 1] == 0 &] (* _Robert G. Wilson v_, Nov 26 2004 *)

%Y Cf. A000045, A100993, A023162, A023173, A045468, A069106.

%K nonn

%O 1,1

%A _Ron Knott_, Nov 25 2004

%E More terms from _Robert G. Wilson v_, Nov 26 2004

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Last modified May 13 11:43 EDT 2024. Contains 372504 sequences. (Running on oeis4.)