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Search: id:A130588
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| A130588 |
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Integers which are not the sum of a 3-almost prime and a prime. |
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+0
1
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| 2, 3, 4, 5, 6, 7, 8, 9, 12, 16, 18, 24, 26, 28, 36, 42, 60, 84, 90, 96, 114, 300
(list; graph; listen)
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OFFSET
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2,1
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COMMENT
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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., 2-almost 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.
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FORMULA
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{n such that for no integers i, j is it the case that A014612(i) + A000040(j) = n}.
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EXAMPLE
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n<10 are in this sequence because the smallest 3-almost prime is 8, hence the smallest 3-almost prime plus prime is 10 = 8 + 2. We have that 282 is not in this sequence because 282 = 125 + 157 = A014612(30) + A000040(37).
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CROSSREFS
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Cf. A000040, A001358, A014612, A064653.
Adjacent sequences: A130585 A130586 A130587 this_sequence A130589 A130590 A130591
Sequence in context: A048381 A115569 A064653 this_sequence A079238 A079042 A114440
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KEYWORD
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more,nonn,fini
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AUTHOR
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Jonathan Vos Post (jvospost3(AT)gmail.com), Jun 16 2007
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