A078742 a(n) = smallest Fibonacci number > a(n-1) such that a(1) + ... + a(n) is prime.

2, 3, 8, 34, 144, 46368, 8944394323791464, 16641027750620563662096, 298611126818977066918552, 146178119651438213260386312206974243796773058, 1065113236465588309403889415460645093083860991848425732542338227915288346612042420944981983005010603735148681490199640832

Offset

1,1

Comments

a(12) to a(17) are approximately 3.132021800*10^349, 1.533208298*10^370, 8.068341610*10^400, 1.144126295*10^609, 1.293644115*10^4898, 1.000900690*10^5142 respectively. - Robert Israel, May 20 2014

Links

Table of n, a(n) for n=1..11.

Formula

a(n) = A000045(A078743(n)). Robert Israel, May 20 2014

Example

a(1)=2, the smallest Fibonacci number to be prime. The smallest Fibonacci number >2 that yields a prime when added to 2 is 3, so a(2)=3. The smallest Fibonacci number > 3 that yields a prime when added to 2+3 is 8 so a(3)=8.

Maple

N:= 14; # to get the first N terms
fib:= combinat[fibonacci]:
a[1]:= 3: s:= fib(3): count:= 1:
for i from 4 while count < N do
   if isprime(s+fib(i)) then
     count:= count+1;
     a[count]:= i;
     s:= s + fib(i);
   fi
od:
seq(fib(a[i]), i=1..N); # Robert Israel, May 20 2014

Crossrefs

Cf. A000045, A078727, A078743.

Sequence in context: A082569 A340495 A084908 * A005370 A112866 A041657

Adjacent sequences: A078739 A078740 A078741 * A078743 A078744 A078745

Keyword

nonn

Author

Neil Fernandez, Dec 21 2002

Extensions

More terms from Robert Israel, May 20 2014

Status

approved