A121927 Minimum k>0 such that Sum[ Fibonacci[i]*k^(i-1), {i,1,n} ] is prime.

1, 2, 1, 6, 10, 39, 6, 44, 165, 2, 8, 23, 50, 18, 30, 1634, 232, 80, 1070, 6, 16, 48, 108, 3, 244, 5254, 232, 49910, 15946, 270, 240, 92, 15, 14, 308, 60, 4, 31980, 2460, 224, 646, 226, 626, 144, 3, 1932, 3528, 766, 6424, 36

Offset

2,2

Comments

For n>0 Fibonacci numbers are A000045[n] = {1,1,2,3,5,8,13,21,34,55,89,...}. Let f(k,n) = Sum[ Fibonacci[i]*k^(i-1), {i,1,n} ]. a(2) = 1 because f(1,2) = 1*1 + 1 = 2 is prime. 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. a(4) = 1 because f(1,4) = 3*1^3 + 2*1^2 + 1*1 + 1 = 7 is prime. Corresponding smallest primes of the form f(k,n) or f((a(n),n) = Sum[ Fibonacci[i]*a(n)^(i-1), {i,1,n} ] are {2,11,7,7207,853211,46477210729,6554599,484440107670157,...}.

Links

Table of n, a(n) for n=2..51.

Crossrefs

Cf. A000045.

Sequence in context: A069114 A173773 A305512 * A200265 A039762 A039795

Adjacent sequences: A121924 A121925 A121926 * A121928 A121929 A121930

Keyword

nonn

Author

Alexander Adamchuk, Sep 02 2006

Status

approved