A352124 Fibonacci numbers k such that pi(k) is also a Fibonacci number.

0, 1, 2, 3, 5, 21, 144

Offset: 1

Author

Marc Kouyoumdjian, Mar 05 2022

Keywords

• nonn
• more

Comments

No examples larger than pi(144) = 34 are known.

Next term is > Fibonacci(123), if it exists (checked using the b-file in A054782). - Amiram Eldar, Mar 05 2022

Examples

			21 is a term because 21 = Fibonacci(8) and pi(21) = 8 = Fibonacci(6).
		

Links

• G. L. Honaker, Jr., Prime Curios!.
• Ron Knott, The Mathematical Magic of Fibonacci Numbers.

Crossrefs

Cf. A000045, A000720, A054782.

Programs

Mathematica

Select[(f = Fibonacci[Join[{0}, Range[2, 20]]]), MemberQ[f, PrimePi[#]] &] (* Amiram Eldar, Mar 05 2022 *)

PARI

isfib(n) = my(k=n^2); k+=(k+1)<<2; issquare(k) || (n>0 && issquare(k-8));
lista(nn) = for (n=0, nn, if (n!=1, my(k=fibonacci(n)); if (isfib(primepi(k)), print1(k, ", ")))); \\ Michel Marcus, Mar 07 2022