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Numbers n such that Fibonacci(n) == 0 (mod triangular(n)).
2

%I #11 Sep 08 2022 08:45:27

%S 1,10,60,108,180,240,250,540,600,660,768,1008,1200,1320,1620,1800,

%T 1860,2160,2520,2688,2736,3000,3060,3300,3360,3528,3888,4200,4800,

%U 4860,4968,5050,5280,5520,5580,5880,6120,6480,6600,6720,6840,7320,7560,7680,8100

%N Numbers n such that Fibonacci(n) == 0 (mod triangular(n)).

%C Zero terms of A121343.

%H Giovanni Resta, <a href="/A121874/b121874.txt">Table of n, a(n) for n = 1..1000</a>

%F Numbers n where A000045(n) == 0 (mod A000217(n)).

%t Select[Range@10000, Mod[Fibonacci@#, #(# + 1)/2] == 0 &]

%o (PARI) for(n=1, 8250, if(Mod(fibonacci(n), binomial(n+1,2))==0, print1(n", "))) \\ _G. C. Greubel_, Oct 08 2019

%o (Magma) [n: n in [1..8250] | Fibonacci(n) mod Binomial(n+1,2) eq 0]; // _G. C. Greubel_, Oct 08 2019

%o (Sage) [n for n in (1..8500) if Mod(fibonacci(n), binomial(n+1,2))==0] # _G. C. Greubel_, Oct 08 2019

%o (GAP) Filtered([1..8250], n-> (Fibonacci(n) mod Binomial(n+1,2))=0 ); # _G. C. Greubel_, Oct 08 2019

%Y Cf. A121343, A000045, A000217.

%K nonn

%O 1,2

%A _Robert G. Wilson v_, Aug 31 2006