A038773 a(n) is the smallest prime of the form Q + c, where Q is the n-th primorial and c is a composite >= prime(n+1)^2.

11, 31, 79, 331, 2531, 30319, 511039, 9700357, 223093769, 6469694377, 200560491721, 7420738136831, 304250263529059, 13082761331672803, 614889782588494961, 32589158477190048817, 1922760350154212643889, 117288381359406970988027, 7858321551080267055884131, 557940830126698960967422909

Offset

1,1

Comments

Between 2310 and 2531 there are 26 primes (2311, ..., 2521), all of which are of the form (primorial + prime). (2311 = 2 + 2309 (prime) = 2*3*5 + 2281 (prime); each of the other 25 primes is of the form 2*3*5*7*11 + prime.)

Observe that a(2) = 31 = 2*3 + 5^2 = 2*3*5 + 1, so it has two "primorial forms".

Links

Michael De Vlieger, Table of n, a(n) for n = 1..100

Example

At n=5, the 5th primorial is A002110(5)=2310 and 2310 + 13*17 = 2310 + 221 = 2531 is the prime that meets the criteria of the definition.

Mathematica

Array[Block[{Q = Product[Prime@ i, {i, #}], c = Prime[# + 1]^2}, While[Nand[PrimeQ[Q + c], CompositeQ@ c], c++]; Q + c] &, 17] (* Michael De Vlieger, May 22 2018 *)

Prog

(PARI) a(n) = {my(pr = prod(k=1, n, prime(k)), c = prime(n+1)^2); while (isprime(c) || !isprime(pr + c), c++); pr + c; } \\ Michel Marcus, May 26 2018

Crossrefs

Cf. A002110, A054757, A054758, A005235.

Sequence in context: A293659 A089346 A296969 * A054757 A038768 A269789

Adjacent sequences: A038770 A038771 A038772 * A038774 A038775 A038776

Keyword

nonn

Author

Labos Elemer, May 04 2000

Extensions

Edited by Jon E. Schoenfield, May 22 2018

More terms from Michael De Vlieger, May 22 2018

Status

approved