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 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. 2
 11, 31, 79, 331, 2531, 30319, 511039, 9700357, 223093769, 6469694377, 200560491721, 7420738136831, 304250263529059, 13082761331672803, 614889782588494961, 32589158477190048817, 1922760350154212643889, 117288381359406970988027, 7858321551080267055884131, 557940830126698960967422909 (list; graph; refs; listen; history; text; internal format)
 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

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Last modified August 24 22:49 EDT 2019. Contains 326314 sequences. (Running on oeis4.)