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

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

Offset

1,3

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

Links

Table of n, a(n) for n=1..7.

G. L. Honaker, Jr., Prime Curios!.

Ron Knott, The Mathematical Magic of Fibonacci Numbers.

Example

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

Mathematica

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

Prog

(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

Crossrefs

Cf. A000045, A000720, A054782.

Sequence in context: A060321 A351989 A093522 * A093499 A339228 A013639

Adjacent sequences: A352121 A352122 A352123 * A352125 A352126 A352127

Keyword

nonn,more

Author

Marc Kouyoumdjian, Mar 05 2022

Status

approved