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).

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

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