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%I #9 May 20 2014 23:37:34
%S 3,4,6,9,12,24,78,108,114,213,576,1674,1773,1920,2916,23439,24606
%N 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.
%C 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
%e 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.
%p N:= 16; # to get the first N terms
%p fib:= combinat[fibonacci]:
%p a[1]:= 3: s:= fib(3): count:= 1:
%p for i from 4 while count < N do
%p if isprime(s+fib(i)) then
%p count:= count+1;
%p a[count]:= i;
%p s:= s + fib(i);
%p fi
%p od:
%p seq(a[i],i=1..N); # _Robert Israel_, May 20 2014
%Y Cf. A000045, A078742.
%K nonn
%O 1,1
%A _Neil Fernandez_, Dec 21 2002
%E a(7) to a(17) from _Robert Israel_, May 20 2014
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