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