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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
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 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,1

COMMENTS

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.

LINKS

Robert Israel, Table of n, a(n) for n = 1..10000

Mathematics StackExchange, Can every odd number be represented as 2pq-r where p, q, and r are distinct odd primes?

EXAMPLE

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.

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

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Last modified August 1 03:05 EDT 2021. Contains 346379 sequences. (Running on oeis4.)