A326422 Numbers k such that A000045(k) mod 5 is prime.

3, 4, 6, 7, 13, 14, 16, 17, 23, 24, 26, 27, 33, 34, 36, 37, 43, 44, 46, 47, 53, 54, 56, 57, 63, 64, 66, 67, 73, 74, 76, 77, 83, 84, 86, 87, 93, 94, 96, 97, 103, 104, 106, 107, 113, 114, 116, 117, 123, 124, 126, 127, 133, 134, 136, 137, 143, 144, 146, 147, 153, 154, 156, 157

Offset: 1

Author

Vincenzo Librandi, Jul 06 2019

Keywords

• nonn
• easy

Comments

Position of prime numbers in A082116.

Links

• Vincenzo Librandi, Table of n, a(n) for n = 1..3740
• Index entries for linear recurrences with constant coefficients, signature (1,0,0,1,-1).

Crossrefs

Cf. A000045, A082116.

Partial sums of A010123.

Programs

Magma

[n: n in [0..200] | IsPrime(Fibonacci(n) mod 5)];

Mathematica

Select[Range[160], MemberQ[{2, 3}, Mod[Fibonacci[#], 5]] &]

Formula

G.f.: x*(3*x^2+4*x+3)*(x^2-x+1)/((x+1)*(x^2+1)*(x-1)^2). - Alois P. Heinz, Jul 08 2019

E.g.f.: (6 - 2*cos(x) + (5*x - 4)*cosh(x) + 2*sin(x) + (5*x - 1)*sinh(x))/2. - Stefano Spezia, Jul 15 2025