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%I #19 Jan 02 2022 00:10:10
%S 1,19,19,43,17,43,1,31,41,43,137,199,103,59,79,103,67,439,331,191,233,
%T 617,211,263,881,131,617,113,761,499,1913,163,467,401,1831,1831,229,
%U 397,1451,853,449,797,1553,239,2383,1049,401,367,2441,613,691,1567,971,3613,1249,1259,811,617,3089
%N 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.
%C Primorial(n) is the product of the first n primes (A002110), while prime(n) is the n-th prime.
%C The first 150000 terms are all either 1 or prime. In the first 150000 terms, this sequence generates 142977 unique primes.
%C a(n) = 1 for n = 1, 7, 232, 430 ... When a(n) > 1, it is greater than prime(n).
%H Dmitry Kamenetsky, <a href="/A323177/b323177.txt">Table of n, a(n) for n = 1..150000</a>
%H Carlos Rivera, <a href="https://www.primepuzzles.net/puzzles/puzz_937.htm">Puzzle 937: A non-composite sequence?</a>.
%e 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.
%t 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 *)
%Y Cf. A002110 (primorial).
%K nonn
%O 1,2
%A _Dmitry Kamenetsky_, Jan 06 2019
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