A038767 Numbers k for which k-th primorial + square of (k+1)-th prime is also a prime.

1, 2, 3, 4, 6, 13, 19, 28, 41, 66, 85, 371, 437, 726, 924, 1063, 3401, 6714

Offset

1,2

Comments

r = prime(n+1)^2 is the smallest possible composite number that, if added to the n-th primorial, might give a prime.

Links

Table of n, a(n) for n=1..18.

Formula

a(n) = A002110(n) + prime(n+1)^2 is prime; n so that A054758(n)=1.

Example

a(5)=6, 6th primorial is 30030, square of 7th prime is 289, sum gives 30319, a prime.

Mathematica

Block[{a = {}, p = 1, q = 1}, Do[q = NextPrime[q]; If[PrimeQ[p + q^2], AppendTo[a, i]]; p *= q, {i, 1200}]; Rest[a] - 1] (* Michael De Vlieger, Jan 03 2021 *)

Prog

(PARI) isok(n) = ispseudoprime(prime(n+1)^2 + prod(j=1, n, prime(j))); \\ Michel Marcus, Aug 26 2019

Crossrefs

Cf. A002110, A054758, A106155, A245694.

Sequence in context: A096988 A066463 A073146 * A363198 A188715 A369849

Adjacent sequences: A038764 A038765 A038766 * A038768 A038769 A038770

Keyword

nonn,more

Author

Labos Elemer, May 04 2000

Extensions

a(12)-a(14) from Michel Marcus, Aug 26 2019

a(15)-a(16) (due to Jon E. Schoenfield at A245694) from Bill McEachen, Jan 03 2021

a(17) from Michael S. Branicky, Jun 09 2023

a(18) from Michael S. Branicky, Aug 09 2024

Status

approved