A329532 Numbers k such that Product_{j=1..k} prime(j) + Product_{j=k+1..2*k} prime(j) is prime.

1, 2, 3, 4, 24, 25, 45, 59, 1238, 2635, 4209, 5341

Offset

1,2

Comments

Based on discussion in primenumbers Yahoo group dated May 12, 2004, with a(9) = 1238 given by Jens Kruse Andersen.

Numbers k > 0 such that A002110(k) + A002110(2*k)/A002110(k) is prime. - Daniel Suteu, Nov 22 2019 [Edited by Michael S. Branicky, Apr 17 2025; else, 0 would be a term since A002110(0)=1 yields prime 2.]

a(13) > 10^4. - Michael S. Branicky, Apr 19 2025

Links

Table of n, a(n) for n=1..12.

Cashogor, Payam Samidoost, David Cleaver, Jens Kruse Andersen, Creating Primes, digest of 9 messages in primenumbers Yahoo group, May 12, 2004. [Cached copy]

Prog

(PARI) for (k=1, 100, if (ispseudoprime(prod(j=1, k, prime(j))+prod(j=k+1, k+k, prime(j))), print1(k, ", ")))

Crossrefs

Cf. A093429.

Sequence in context: A010345 A233344 A329566 * A265484 A000336 A287433

Adjacent sequences: A329529 A329530 A329531 * A329533 A329534 A329535

Keyword

nonn,hard,more

Author

Hugo Pfoertner, Nov 15 2019

Extensions

a(10) from Daniel Suteu, Nov 22 2019

a(11)-a(12) from Michael S. Branicky, Apr 17 2025

Status

approved