A248033 Least number k such that k + n divides F(n)^2 + F(k)^2.

1, 3, 2, 1, 5, 19, 18, 17, 16, 3, 14, 12, 4, 11, 10, 9, 8, 7, 6, 5, 4, 3, 2, 1, 25, 99, 98, 9, 36, 95, 94, 93, 92, 91, 90, 12, 88, 23, 50, 10, 68, 83, 22, 81, 80, 79, 11, 24, 76, 15, 74, 73, 5, 71, 18, 29, 8, 67, 66, 12, 28, 63, 62, 1, 20, 47, 58, 41, 56, 40, 54, 17, 24, 11, 50, 49, 48

Offset

1,2

Comments

F(n) denotes the n-th Fibonacci number. I believe a(n) exists for all n > 0.

Links

Table of n, a(n) for n=1..77.

Mathematica

a[n_]:=Module[{k=1}, While[!Divisible[Fibonacci[n]^2+Fibonacci[k]^2, k+n], k++]; k]; Array[a, 77] (* Stefano Spezia, Oct 12 2025 *)

Prog

(PARI)
a(n)=m=1; while((fibonacci(n)^2+fibonacci(m)^2)%(m+n), m++); m
vector(100, n, a(n))

Crossrefs

Cf. A000045, A247937, A248032.

Sequence in context: A144252 A389708 A396676 * A318254 A002130 A382347

Adjacent sequences: A248030 A248031 A248032 * A248034 A248035 A248036

Keyword

nonn

Author

Derek Orr, Sep 29 2014

Status

approved