A178837 - OEIS

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

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OFFSET

1,1

LINKS

Table of n, a(n) for n=1..62.

EXAMPLE

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.

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:

# Alternative:

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 *)

CROSSREFS

Cf. A000045, A065398.

Sequence in context: A047601 A029675 A030310 * A217288 A212011 A207005

Adjacent sequences: A178834 A178835 A178836 * A178838 A178839 A178840

KEYWORD

nonn,base

AUTHOR

Michel Lagneau, Jun 17 2010

STATUS

approved