A215011 a(n) = least k>0 such that triangular(n) divides Fibonacci(k).

1, 4, 12, 15, 20, 8, 24, 12, 60, 10, 60, 84, 56, 40, 60, 18, 36, 36, 90, 120, 40, 120, 24, 300, 175, 252, 72, 168, 140, 60, 60, 60, 180, 360, 120, 228, 342, 252, 420, 60, 40, 88, 660, 60, 120, 48, 48, 168, 1400, 900, 252, 189, 108, 180, 120, 72, 252, 406, 1740

Offset: 1

Author

Alex Ratushnyak, Aug 08 2012

Keywords

• nonn

Comments

Triangular(n)=n*(n+1)/2 is the n-th triangular number.

Examples

			Triangular(2)=3, least k>0 such that 3 divides Fibonacci(k) is k=4, so a(2)=4.
		

Crossrefs

Cf. A085779 (least k such that triangular(n) divides k!).

Cf. A001177 (least k such that n divides Fibonacci(k)).

Cf. A132632 (least k such that n^2 divides Fibonacci(k)).

Cf. A132633 (least k such that n^3 divides Fibonacci(k)).

Cf. A215453 (least k such that n^n divides Fibonacci(k)).

Cf. A214528 (least k such that n! divides Fibonacci(k)).

Cf. A000217, A000045.

Programs

Mathematica

lk[n_]:=Module[{k=1,t=(n(n+1))/2},While[Mod[Fibonacci[k],t]!=0,k++];k]; Array[lk,60] (* Harvey P. Dale, Jun 19 2021 *)

Python

TOP = 333
prpr = y = 0
prev = k = 1
res = [-1]*TOP
while y