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URL: https://oeis.org/A153887

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A153887
Smallest of five consecutive Fibonacci numbers whose sum is a prime number.
5
0, 1, 2, 8, 89, 144, 2584, 121393, 196418, 832040, 20365011074, 4052739537881, 8944394323791464, 99194853094755497, 2880067194370816120, 14028366653498915298923761, 96151855463018422468774568
OFFSET
1,3
COMMENTS
0+1+1+2=3=7, 1+2+3+5+8=19, 2+3+5+8=13=31, 8+13+21+34+55=131, 89+144+233+377+610=1453, 144+233+377+610+987=2351,...
FORMULA
For n>=3, a(n) + A000032(m+4) is prime, where m is the Fibonacci index of a(n) (see example). This follows from the identity F(m+1) + F(m+2) + F(m+3) + F(m+4) = A000032(m+4), m>=0. - Vladimir Shevelev, Apr 24 2014
EXAMPLE
For n=3,4, the Fibonacci indices of a(3)=2, a(4)=8, are 3,6 respectively. So a(3) + A000032(7)= 31, a(4) + A000032(10) = 131. - Vladimir Shevelev, Apr 24 2014
MATHEMATICA
a=0; b=1; c=1; d=2; lst={}; Do[e=Fibonacci[n]; p=a+b+c+d+e; If[PrimeQ[p], AppendTo[lst, a]]; a=b; b=c; c=d; d=e, {n, 4, 6!}]; lst
Select[Partition[Fibonacci[Range[1000]], 5, 1], PrimeQ[Total[#]]&][[All, 1]] (* Harvey P. Dale, Dec 01 2016 *)
KEYWORD
nonn
AUTHOR
STATUS
approved