|
%I #14 Dec 01 2016 15:50:26
%S 0,1,2,8,89,144,2584,121393,196418,832040,20365011074,4052739537881,
%T 8944394323791464,99194853094755497,2880067194370816120,
%U 14028366653498915298923761,96151855463018422468774568
%N Smallest of five consecutive Fibonacci numbers whose sum is a prime number.
%C 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,...
%F 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
%e 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
%t 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
%t Select[Partition[Fibonacci[Range[1000]],5,1],PrimeQ[Total[#]]&][[All,1]] (* _Harvey P. Dale_, Dec 01 2016 *)
%Y Cf. A000045, A001906, A000071, A001605, A153862, A153863, A153865, A153866, A153867.
%K nonn
%O 1,3
%A _Vladimir Joseph Stephan Orlovsky_, Jan 03 2009
|
