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A329951 a(n) is the least prime k such that 2*n-1+k = 2*p*q for odd primes p,q (not necessarily distinct). 1

%I

%S 17,47,13,11,41,7,5,3,13,11,29,7,5,3,13,11,17,7,5,3,29,7,5,3,17,19,13,

%T 11,13,7,5,3,5,3,29,7,5,3,37,19,17,19,13,11,13,7,5,3,5,3,13,7,5,3,5,3,

%U 17,23,13,11,17,7,5,3,41,7,5,3,17,31,13,11,29,7,5,3,17,19,13,11,13,7,5,3,5

%N a(n) is the least prime k such that 2*n-1+k = 2*p*q for odd primes p,q (not necessarily distinct).

%C Dickson's conjecture implies that for every prime p that does not divide 2*n-1, there exist infinitely many q such that q and 2*p*q-(2*n-1) are prime. Thus a(n) always exists.

%H Robert Israel, <a href="/A329951/b329951.txt">Table of n, a(n) for n = 1..10000</a>

%H Mathematics StackExchange, <a href="https://math.stackexchange.com/questions/3450575">Can every odd number be represented as 2pq-r where p, q, and r are distinct odd primes?</a>

%e a(3)=13 because 2*3-1+13 = 18 = 2*3*3 with 13, 3, 3 all primes, and 13 is the least prime for which this works.

%p f:= proc(m) local r,x;

%p r:= 2:

%p do r:= nextprime(r);

%p x:= (m+r)/2;

%p if x::odd and numtheory:-bigomega(x)=2 then return r

%p fi od

%p end proc:

%p map(f, [seq(i,i=1..1000,2)]);

%K nonn

%O 1,1

%A _Robert Israel_, Nov 25 2019

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Last modified September 20 17:42 EDT 2021. Contains 347588 sequences. (Running on oeis4.)