A178837 Indices k such that the sum of the digits of Fibonacci(k) is a prime number.

3, 4, 5, 8, 9, 11, 14, 15, 18, 22, 25, 26, 27, 29, 30, 31, 34, 39, 41, 43, 45, 47, 51, 53, 54, 58, 61, 63, 65, 66, 67, 81, 85, 87, 90, 94, 99, 105, 107, 111, 113, 118, 122, 133, 135, 139, 147, 149, 151, 161, 167, 169, 173, 187, 191, 193, 194, 195, 198, 202, 213, 223

Offset: 1

Author

Michel Lagneau, Jun 17 2010

Keywords

• nonn
• base

Examples

			3 is in the sequence because Fibonacci(3) = 2, and 2 is prime.
113 is in the sequence because Fibonacci(113) = 184551825793033096366333 and the sum of the digits = 103 is prime.
		

Crossrefs

Cf. A000045, A065398.

Programs

Maple

with(combinat, fibonacci):nn:= 120: for n from 1 to 700 do:p:=fibonacci(n):l:=length(p):n0:=p:s:=0:for m from 1 to l do:q:=n0:u:=irem(q, 10):v:=iquo(q, 10):n0:=v :s:=s+u:od:if type(s, prime)=true then printf(`%d, `, n): else fi:od:
# second Maple program:
q:= n-> isprime(add(i, i=convert(combinat[fibonacci](n), base, 10))):
select(q, [$0..223])[];  # Alois P. Heinz, Jul 15 2025

Mathematica

Select[Range[300],PrimeQ[Total[IntegerDigits[Fibonacci[#]]]]&] (* Harvey P. Dale, Oct 22 2017 *)