A323177 a(n) = X * prime(n+1) - B, where B = primorial(n) and X is the smallest number that is larger than B/prime(n+1) and coprime to B.

1, 19, 19, 43, 17, 43, 1, 31, 41, 43, 137, 199, 103, 59, 79, 103, 67, 439, 331, 191, 233, 617, 211, 263, 881, 131, 617, 113, 761, 499, 1913, 163, 467, 401, 1831, 1831, 229, 397, 1451, 853, 449, 797, 1553, 239, 2383, 1049, 401, 367, 2441, 613, 691, 1567, 971, 3613, 1249, 1259, 811, 617, 3089

Offset

1,2

Comments

Primorial(n) is the product of the first n primes (A002110), while prime(n) is the n-th prime.

The first 150000 terms are all either 1 or prime. In the first 150000 terms, this sequence generates 142977 unique primes.

a(n) = 1 for n = 1, 7, 232, 430 ... When a(n) > 1, it is greater than prime(n).

Links

Dmitry Kamenetsky, Table of n, a(n) for n = 1..150000

Carlos Rivera, Puzzle 937: A non-composite sequence?.

Example

When n = 4, primorial(n) = 210, primorial(n)/prime(n+1) = 210/11 ~= 19.09..., thus X = 23 and a(n) = 23*11 - 210 = 43.

Mathematica

Array[Block[{p = #1, B = #2, X = Floor[#2/#1] + 1}, While[GCD[B, X] != 1, X++]; X p - B] & @@ {First@ #1, Times @@ #2} & @@ TakeDrop[Prime@ Range@ #, -1] &, 60, 2] (* Michael De Vlieger, Jan 07 2019 *)

Crossrefs

Cf. A002110 (primorial).

Sequence in context: A272897 A040343 A022353 * A261756 A070853 A165840

Adjacent sequences: A323174 A323175 A323176 * A323178 A323179 A323180

Keyword

nonn

Author

Dmitry Kamenetsky, Jan 06 2019

Status

approved