A386743 For n >= 0, a(n) is the least Fibonacci number F(i) such that F(i) = (2*n + 1)*(n + k) for some k >= 0.

0, 3, 55, 21, 144, 55, 377, 6765, 2584, 2584, 987, 46368, 75025, 14930352, 317811, 832040, 6765, 102334155, 4181, 317811, 6765, 701408733, 1548008755920, 2178309, 225851433717, 14930352, 196418, 6765, 14930352, 591286729879, 832040, 46368, 9227465, 72723460248141, 46368

Offset: 0

Author

Ctibor O. Zizka, Aug 01 2025

Keywords

• nonn

Comments

a(n) >= n*(2*n + 1).

Empirical observation: For F(i), i is from {1/3, 1/2, 2/3, 1, 3/2, 2}*A001177(2*n + 1).

Examples

			For n = 3: F(i) = 21 + 7*k is true for k = 0, F(8) = 21, thus a(3) = 21.
		

Crossrefs

Cf. A000045, A001177.

Programs

Mathematica

a[n_]:=Module[{i=0},While[!Divisible[Fibonacci[i],2n+1] || Fibonacci[i]/(2n+1) < n, i++]; Fibonacci[i]]; Array[a,35,0] (* Stefano Spezia, Aug 04 2025 *)

PARI

a(n) = my(i=0, f=fibonacci(0)); while((f % (2*n+1)) || (f/(2*n+1) < n), i++; f=fibonacci(i)); f; \\ Michel Marcus, Aug 01 2025

Python

def A386743(n):
    a, b, m, k = 0, 1, n*((n<<1)|1), (n<<1)|1
    while aChai Wah Wu, Aug 11 2025

Extensions

More terms from Michel Marcus, Aug 01 2025