

A038767


Numbers n for which nth primorial + square of (n+1)th prime is also a prime.


0



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

1,2


COMMENTS

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


LINKS

Table of n, a(n) for n=1..16.


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, A245694.
Sequence in context: A096988 A066463 A073146 * A188715 A174046 A095991
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


STATUS

approved



