

A130588


Integers which are not the sum of a 3almost prime and a prime.


6



2, 3, 4, 5, 6, 7, 8, 9, 12, 16, 18, 24, 26, 28, 36, 42, 60, 84, 90, 96, 114, 300
(list;
graph;
refs;
listen;
history;
text;
internal format)



OFFSET

2,1


COMMENTS

T. D. Noe found no more values up to 10000 and agrees with my conjecture that this sequence is probably finite. This is related to Chen's Theorem: "Every 'large' even number may be written as 2n = p + m where p is a prime and m in A001358 is the set of semiprimes (i.e., 2almost primes)" which itself is related to Goldbach's conjecture. However, we have no proof, merely the sense that it gets easier and easier to find more and more A014612(i) + A000040(j) = n decompositions as n increases.


LINKS

Table of n, a(n) for n=2..23.


FORMULA

{n such that for no integers i, j is it the case that A014612(i) + A000040(j) = n}.


EXAMPLE

n<10 are in this sequence because the smallest 3almost prime is 8, hence the smallest 3almost prime plus prime is 10 = 8 + 2. We have that 282 is not in this sequence because 282 = 125 + 157 = A014612(30) + A000040(37).


MATHEMATICA

Rest@Complement[Range[1000], Union@Flatten@Outer[Plus, Select[Range[1000], PrimeOmega[#] == 3 &], Prime[Range[PrimePi[1000]]]]] (* Robert Price, Jun 16 2019 *)


CROSSREFS

Cf. A000040, A001358, A014612, A064653.
Sequence in context: A185186 A115569 A064653 * A079238 A079042 A193455
Adjacent sequences: A130585 A130586 A130587 * A130589 A130590 A130591


KEYWORD

more,nonn,fini


AUTHOR

Jonathan Vos Post, Jun 16 2007


STATUS

approved



