

A329951


a(n) is the least prime k such that 2*n1+k = 2*p*q for odd primes p,q (not necessarily distinct).


1



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, 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, 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
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OFFSET

1,1


COMMENTS

Dickson's conjecture implies that for every prime p that does not divide 2*n1, there exist infinitely many q such that q and 2*p*q(2*n1) are prime. Thus a(n) always exists.


LINKS

Robert Israel, Table of n, a(n) for n = 1..10000
Mathematics StackExchange, Can every odd number be represented as 2pqr where p, q, and r are distinct odd primes?


EXAMPLE

a(3)=13 because 2*31+13 = 18 = 2*3*3 with 13, 3, 3 all primes, and 13 is the least prime for which this works.


MAPLE

f:= proc(m) local r, x;
r:= 2:
do r:= nextprime(r);
x:= (m+r)/2;
if x::odd and numtheory:bigomega(x)=2 then return r
fi od
end proc:
map(f, [seq(i, i=1..1000, 2)]);


CROSSREFS

Sequence in context: A307293 A045570 A058205 * A034783 A275770 A126912
Adjacent sequences: A329948 A329949 A329950 * A329952 A329953 A329954


KEYWORD

nonn


AUTHOR

Robert Israel, Nov 25 2019


STATUS

approved



