A123371 Smallest number k>1 such that (1 + Sum[ i^(2n - 1), {i,1,k} ]) is prime, or 0 if no such number k exists.

3, 3, 3, 4, 35, 16, 7, 4, 11, 55, 112, 183, 36, 51, 23, 56, 8, 16, 32, 28, 115, 135, 44, 15, 28, 111, 43, 364, 80, 44, 144, 59, 3, 48, 68, 75, 63, 48, 175, 228, 416, 39, 163, 251, 7, 331, 35, 4, 412, 4, 152, 63, 483, 11, 239, 75, 47, 11, 32, 3, 163, 211, 44, 40, 155, 555

Offset

1,1

Comments

Conjecture: a(n)>0 exists for all n.

Links

Table of n, a(n) for n=1..66.

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

Sequence in context: A266688 A347139 A285286 * A011277 A376659 A084742

Adjacent sequences: A123368 A123369 A123370 * A123372 A123373 A123374

Keyword

hard,nonn,changed

Author

Alexander Adamchuk, Nov 09 2006

Status

approved