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A323177 a(n) = X * prime(n+1) - B, where B = primorial(n) and X is the smallest number bigger than B/prime(n+1) and coprime to B. 1
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 (list; graph; refs; listen; history; text; internal format)
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

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Last modified October 28 16:41 EDT 2021. Contains 348329 sequences. (Running on oeis4.)