A121927 - OEIS

%I #6 Sep 15 2024 06:52:06

%S 1,2,1,6,10,39,6,44,165,2,8,23,50,18,30,1634,232,80,1070,6,16,48,108,

%T 3,244,5254,232,49910,15946,270,240,92,15,14,308,60,4,31980,2460,224,

%U 646,226,626,144,3,1932,3528,766,6424,36

%N Minimum k>0 such that Sum_{i=1..n} Fibonacci(i)*k^(i-1) is prime.

%C Let f(k,n) = Sum_{i=1..n} Fibonacci(i)*k^(i-1) where Fibonacci(i) = A000045(i). Corresponding smallest primes of the form f(k,n) or f(a(n),n) are {2,11,7,7207,853211,46477210729,6554599,484440107670157,...}.

%e a(2) = 1 because f(1,2) = 1*1 + 1 = 2 is prime.

%e a(3) = 2 because f(2,3) = 2*2^2 + 1*2 + 1 = 11 is prime but f(1,3) = 2*1^2 + 1*1 + 1 = 4 is not prime.

%e a(4) = 1 because f(1,4) = 3*1^3 + 2*1^2 + 1*1 + 1 = 7 is prime.

%Y Cf. A000045.

%K nonn

%O 2,2

%A _Alexander Adamchuk_, Sep 02 2006