A390108 Smallest b >= 2 for which P_{n}(b) = Sum_{k=1..n} b^(prime(n)-prime(k)) is prime or 0 if such a number does not exist.

0, 2, 2, 2, 0, 20, 12, 46, 17, 2, 4, 296, 137, 6, 5, 582, 16, 258, 49, 330, 2, 140, 145, 2664, 325, 250, 15, 618, 406, 24, 190, 466, 534, 124, 352, 330, 1071, 820, 54, 314, 372, 1500, 137, 2340, 1797, 1320, 1275, 324, 306, 252, 483, 1008, 18, 794, 338, 1224, 462, 46, 1008, 170, 275, 210, 510, 1788

Offset

1,2

Links

Davide Oliveri, Table of n, a(n) for n = 1..313

Example

For n = 6, prime(n) = 13.
P_{13}(b) = b^11 + b^10 + b^8 + b^6 + b^2 + 1.
P_{13}(2) = 3397 = 43 * 79, P_{13}(3) = 60496 (composite), ..., P_{13}(20) = 215065664000401 (prime).
Therefore a(6) = 20.
For n=5 (prime(5)=11), P_11(b) = (b^2 - b + 1)*(b^7 + 2*b^6 + b^5 - b^3 + b + 1) is reducible over Z[b]; thus a(5)=0.

Prog

(PARI) a(n) = if ((n==1) || (n==5), return(0)); my(b=2); while(!ispseudoprime(sum(k=1, n, b^(prime(n)-prime(k)))), b++); b; \\ Michel Marcus, Nov 03 2025

Crossrefs

Cf. A072762, A109227.

Sequence in context: A181230 A262372 A390550 * A392180 A292520 A131079

Adjacent sequences: A390105 A390106 A390107 * A390109 A390110 A390111

Keyword

nonn

Author

Davide Oliveri, Oct 25 2025

Status

approved