A121343 -id:A121343 - cp's OEIS frontend

A121874 Numbers n such that Fibonacci(n) == 0 (mod triangular(n)).

1, 10, 60, 108, 180, 240, 250, 540, 600, 660, 768, 1008, 1200, 1320, 1620, 1800, 1860, 2160, 2520, 2688, 2736, 3000, 3060, 3300, 3360, 3528, 3888, 4200, 4800, 4860, 4968, 5050, 5280, 5520, 5580, 5880, 6120, 6480, 6600, 6720, 6840, 7320, 7560, 7680, 8100

Offset: 1

Robert G. Wilson v, Aug 31 2006

nonn

Zero terms of A121343.

Giovanni Resta, Table of n, a(n) for n = 1..1000

Cf. A121343, A000045, A000217.

Filtered([1..8250], n-> (Fibonacci(n) mod Binomial(n+1,2))=0 ); # G. C. Greubel, Oct 08 2019

[n: n in [1..8250] | Fibonacci(n) mod Binomial(n+1,2) eq 0]; // G. C. Greubel, Oct 08 2019

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

for(n=1, 8250, if(Mod(fibonacci(n), binomial(n+1,2))==0, print1(n", "))) \\ G. C. Greubel, Oct 08 2019

[n for n in (1..8500) if Mod(fibonacci(n), binomial(n+1,2))==0] # G. C. Greubel, Oct 08 2019

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

A217737 a(n) = Fibonacci(n) mod n*(n+1).

Original entry on oeis.org

1, 1, 2, 3, 5, 8, 13, 21, 34, 55, 89, 144, 51, 167, 130, 171, 67, 190, 1, 45, 320, 1, 505, 168, 275, 649, 614, 319, 59, 620, 125, 837, 376, 407, 485, 1296, 1331, 419, 466, 1435, 1231, 1420, 1289, 1653, 830, 2069, 2161, 1344, 1849, 1975, 746, 1167, 1589, 872, 2645, 2205

Offset: 1

Alex Ratushnyak, Mar 22 2013

Alois P. Heinz, Table of n, a(n) for n = 1..10000

Cf. A000045, A002708, A121343, A132634, A132636.

a:= proc(n) local r, M, p, m; r, M, p, m:=
      <<1|0>, <0|1>>, <<0|1>, <1|1>>, n, n*(n+1);
      do if irem(p, 2, 'p')=1 then r:= r.M mod m fi;
         if p=0 then break fi; M:= M.M mod m
      od; r[1, 2]
    end:
seq(a(n), n=1..100);  # Alois P. Heinz, Nov 26 2016

Table[Mod[Fibonacci[n],n(n+1)],{n,60}] (* Harvey P. Dale, Oct 02 2017 *)

a(n)=fibonacci(n)%(n*(n+1)) \\ Charles R Greathouse IV, Jun 23 2017

prpr, prev = 0, 1
for i in range(1, 333):
    cur = prpr + prev
    print(str(prev % (i*(i+1))), end=', ')
    prpr, prev = prev, cur

A000045(n) modulo A002378(n).

A294369 Indices of Fibonacci numbers (A000045) that are triangular numbers (A000217).

Original entry on oeis.org

0, 1, 2, 4, 8, 10

Offset: 1

Alex Ratushnyak, Jan 24 2018

The sequence of Fibonacci numbers that are also triangular numbers begins: 0, 1, 1, 3, 21, 55. That is, 0 and 1 followed by A039595.

			Fibonacci(10)=55 is a triangular number, therefore 10 is in the sequence.

Cf. A000045, A000217, A039595, A162394, A121343, A121874.

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A121874 Numbers n such that Fibonacci(n) == 0 (mod triangular(n)).

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A217737 a(n) = Fibonacci(n) mod n*(n+1).

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A294369 Indices of Fibonacci numbers (A000045) that are triangular numbers (A000217).

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