A383045 Integers k for which the sum of digits of Fibonacci(k) is a Fibonacci number.

0, 1, 2, 3, 4, 5, 6, 8, 13, 28, 33, 49, 85, 94, 107, 286, 299, 366, 421, 422, 443, 657, 2807, 4483, 4531, 18694, 49140, 79033, 79850, 80290, 128306, 129049, 129618, 208245, 338888, 546571, 882766, 883822, 886342

Offset: 1

Author

Michel Marcus, Apr 14 2025

Keywords

• nonn
• base
• more

Examples

			Fibonacci(8) = 21 and sumdigits(21) = 3, a Fibonacci number, so 8 is a term.
		

Crossrefs

Cf. A000045, A020995, A067515, A004090, A178837, A382053.

Programs

Maple

q:= n-> (t-> issqr(t+4) or issqr(t-4))(5*add(i, i=convert(combinat[fibonacci](n), base, 10))^2):
select(q, [$0..4600])[];  # Alois P. Heinz, Jul 15 2025

Mathematica

fibQ[n_] := Or @@ IntegerQ /@ Sqrt[5*n^2 + {-4, 4}]; Select[Range[0, 1000], fibQ[DigitSum[Fibonacci[#]]] &] (* Amiram Eldar, Apr 14 2025 *)

PARI

isfib(n) = my(k=n^2); k+=(k+1)<<2; issquare(k) || (n>0 && issquare(k-8));
isok(k) = isfib(sumdigits(fibonacci(k)));

Extensions

a(36)-a(39) from Amiram Eldar, Apr 14 2025