A065398 -id:A065398 - cp's OEIS frontend

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

Michel Lagneau, Jun 17 2010

			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.

Cf. A000045, A065398.

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

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

A111331 Prime Fibonacci numbers whose digits in base 10 sum up to a prime.

Original entry on oeis.org

2, 3, 5, 89, 514229, 433494437, 2971215073, 3061719992484545030554313848083717208111285432353738497131674799321571238149015933442805665949

Offset: 1

Stefan Steinerberger, Nov 05 2005

Fibonacci(104911) is the next (probable) prime whose digits sum to a prime. Thus the next term would be 21925 digits long. - Hans Havermann, Nov 06 2005

			514229 is a prime Fibonacci number and the sum of the digits 5 + 1 + 4 + 2 + 2 + 9 = 23 is also a prime.

Cf. A065398, A051694, A051694, A067515.

Select[Fibonacci[Range[1000]],PrimeQ[#]&&PrimeQ[Total[IntegerDigits[#]]]&] (* James C. McMahon, May 31 2024 *)

A181364 Fibonacci numbers whose digits, when squared, sum to a prime.

Original entry on oeis.org

21, 377, 610, 2584, 17711, 75025, 196418, 514229, 63245986, 701408733, 1134903170, 1836311903, 2971215073, 17167680177565, 72723460248141, 117669030460994, 2880067194370816120, 19740274219868223167, 354224848179261915075, 1500520536206896083277

Offset: 1

Carmine Suriano, Oct 15 2010

			a(5) = 17711 = Fibonacci(22) since 1^2+7^2+7^2+1^2+1^2 = 1+49+49+1+1 = 101 is prime.

Vincenzo Librandi, Table of n, a(n) for n = 1..200

Intersection of A000045 and A108662.

Cf. A178838, A065398.

Select[Fibonacci[Range[150]],PrimeQ[Total[IntegerDigits[#]^2]]&] (* Harvey P. Dale, Feb 27 2012 *)

a(n) = A000045(A178838(n)). - Michel Marcus, Sep 01 2025

Corrected and extended by Harvey P. Dale, Feb 27 2012

A316527 Fibonacci numbers whose sum of digits is not a prime.

Original entry on oeis.org

0, 1, 8, 13, 55, 144, 233, 987, 1597, 4181, 6765, 10946, 28657, 46368, 317811, 2178309, 3524578, 9227465, 14930352, 24157817, 39088169, 102334155, 267914296, 701408733, 1836311903, 4807526976, 7778742049, 12586269025, 32951280099, 139583862445, 225851433717

Offset: 1

Vincenzo Librandi, Jul 11 2018

Complement of A065398 within A000045.

Cf. A178837.

S:=List(List(List([2..60],Fibonacci),ListOfDigits),Sum);;
a:=[];; for i in [1..Length(S)] do if not IsPrime(S[i]) then Add(a,Fibonacci(i+1)); fi; od; a:=Concatenation([0],a); # Muniru A Asiru, Jul 12 2018

[Fibonacci(n): n in [2..80] | not IsPrime(&+Intseq(Fibonacci(n)))];

Rest[Select[Fibonacci[Range[100]], !PrimeQ[Total[IntegerDigits[#]]]&]]

cp's OEIS Frontend

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

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A111331 Prime Fibonacci numbers whose digits in base 10 sum up to a prime.

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Mathematica

A181364 Fibonacci numbers whose digits, when squared, sum to a prime.

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A316527 Fibonacci numbers whose sum of digits is not a prime.

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