A078743 a(n) is the Fibonacci index of b(n) in the sequence b(1), b(2), ... where b(n) is the smallest Fibonacci number > b(n-1) such that b(1) + ... + b(n) is prime.

3, 4, 6, 9, 12, 24, 78, 108, 114, 213, 576, 1674, 1773, 1920, 2916, 23439, 24606

Offset

1,1

Comments

A more compact version of A078742. a(7), if it exists, > 73, because A078742(7), if it exists, >10^15. - Neil Fernandez, Aug 22 2007

Links

Table of n, a(n) for n=1..17.

Example

The smallest Fibonacci number to be prime is 2, the 3rd Fibonacci number, so a(1)=3. The smallest Fibonacci number >2 that yields a prime when added to 2 is 3, the 4th Fibonacci number, so a(2)=4. The smallest Fibonacci number >3 that yields a prime when added to 2+3 is 8, the 4th Fibonacci number, so a(3)=6.

Maple

  N:= 16; # 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(a[i], i=1..N); # Robert Israel, May 20 2014

Crossrefs

Cf. A000045, A078742.

Sequence in context: A241655 A288346 A373416 * A096846 A140570 A285303

Adjacent sequences: A078740 A078741 A078742 * A078744 A078745 A078746

Keyword

nonn

Author

Neil Fernandez, Dec 21 2002

Extensions

a(7) to a(17) from Robert Israel, May 20 2014

Status

approved