

A299791


2provable primes: Primes p expressible as x+y, where the prime factors of x and y are precisely the primes less than sqrt(p).


0



5, 11, 13, 17, 19, 29, 31, 37, 41, 43, 47, 53, 59, 61, 67, 71, 73, 79, 83, 89, 97, 101, 103, 107, 109, 113, 127, 131, 137, 139, 149, 167
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OFFSET

1,1


COMMENTS

There cannot be any terms > 169 because the least possible value for x+y once 13 is included in the set of prime factors is 347 > 17^2. For p > 347, the list of factors required in x or y also includes 17, pushing the minimal p to 1429 (714 + 715). This in turn adds the next 5 primes to the list, pushing the minimal value of x+y exponentially upward relative to p.


LINKS

Table of n, a(n) for n=1..32.


EXAMPLE

The primes less than sqrt(167) are 2, 3, 5, 7, and 11, and 167 = 2*3*3*5 + 7*11, so 167 is in this sequence.


CROSSREFS

Sequence in context: A288445 A087759 A234644 * A230359 A161548 A090320
Adjacent sequences: A299788 A299789 A299790 * A299792 A299793 A299794


KEYWORD

nonn,fini,full


AUTHOR

Charlie Neder, Jan 21 2019


STATUS

approved



