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A147568
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a(n)=2A000695(n)+3
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2
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3, 5, 11, 13, 35, 37, 43, 45, 131, 133, 139, 141, 163, 165, 171, 173, 515, 517, 523, 525, 547, 549, 555, 557, 643, 645, 651, 653, 675, 677
(list; graph; refs; listen; history; internal format)
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OFFSET
| 0,1
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COMMENTS
| Every odd number m>=9 is a unique sum of the form a(k)+2a(l); moreover this sequence is the unique one with such property. In connection with A103151, note that there is no subsequence T of primes such that every odd number m>=9 is expressible as a unique sum of the form m=p+2q, where p and q are in T. One can prove that if one replaces 9 by any integer x_o>9, the statement remains true (see the preprint arxiv.org/abs/0811.0290).
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CROSSREFS
| Cf. A000695 A062880 A103151
Sequence in context: A095082 A105071 A089251 * A006794 A032457 A122564
Adjacent sequences: A147565 A147566 A147567 * A147569 A147570 A147571
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KEYWORD
| nonn
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AUTHOR
| Vladimir Shevelev (shevelev(AT)bgu.ac.il), Nov 07 2008
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EXTENSIONS
| Instead of "we conjecture" I wrote "one can prove". - Vladimir Shevelev (shevelev(AT)bgu.ac.il), Nov 10 2008
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