OFFSET
1,1
COMMENTS
Conjecture: a(n)>0 exists for all n.
EXAMPLE
a(1) = 3 because 1 + Sum[ i, {i,1,3} ] = 1 + (1 + 2 + 3) = 7 is prime and 1 + (1 + 2) = 4 is composite.
a(2) = 3 because 1 + Sum[ i^3, {i,1,3} ] = 1 + (1^3 + 2^3 + 3^3) = 37 is prime and 1 + (1^3 + 2^3) = 10 is composite.
MATHEMATICA
s={}; Do[k=1; Until[PrimeQ[1+Sum[i^(2n-1), {i, 1, k}]], k++]; AppendTo[s, k], {n, 66}]; s (* James C. McMahon, Nov 20 2024 *)
CROSSREFS
KEYWORD
hard,nonn,changed
AUTHOR
Alexander Adamchuk, Nov 09 2006
STATUS
approved