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Search: id:A135257
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| A135257 |
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Smallest semiprimes such that a(j) - a(k) are all different. |
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1
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| 4, 6, 9, 10, 21, 34, 55, 65, 74, 94, 141, 177, 203, 219, 298, 321, 395, 403, 529, 581, 635, 662, 731, 934, 982, 1073, 1145, 1317, 1418, 1762, 1769, 1849, 1915, 2066, 2165, 2305, 2327, 2746, 2809, 3127, 3409, 3859, 3983, 4138, 4285, 4559, 4742, 5186, 5299, 5854
(list; graph; listen)
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OFFSET
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1,1
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COMMENT
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Semiprime analogue of A079848. This is the slowest-growing semiprime B2 sequence (see A005282). The difference set through a(n) must have cardinality exactly C(n,2) = n*(n+1)/2 = A000217(n-1).
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EXAMPLE
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a(1) = 4, the smallest semiprime (A001358(1)).
a(2) = 6 = A001358(2); the difference set so far is {2}.
a(3) = 9 = A001358(3); the difference set so far is {2,3,5}.
a(4) = 10 = A001358(4); the difference set so far is {1,2,3,4,5,6}.
a(5) can't be 14 = A001358(5) because 14-10 =4, in the difference set through a(4); can't be 15 = A001358(6) because 15-10 =5, in the difference set through a(4)...
a(5) = 21 = A001358(7); the difference set so far is {1,2,3,4,5,6,11,12,15,17}.
a(6) = 34 = A001358(12); the difference set so far is {1,2,3,4,5,6,11,12,13,15,17,24,25,28,30}.
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MAPLE
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A135257 := proc(nmax) local a, anext, diffset, good, an ; a := [4, 6] ; diffset := {2} ; while nops(a) < nmax do for anext from op(-1, a)+1 do if numtheory[bigomega](anext) = 2 then good := true ; for an in a do if ( anext-an) in diffset then good := false ; break ; fi ; od; if good then for an from 1 to nops(a) do diffset := diffset union { anext-op(an, a) } ; od; a := [op(a), anext] ; break ; fi ; fi ; od ; od: a ; end: A135257(60) ; - R. J. Mathar (mathar(AT)strw.leidenuniv.nl), Jan 08 2008
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CROSSREFS
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Cf. A000217, A001358, A005282, A079848.
Adjacent sequences: A135254 A135255 A135256 this_sequence A135258 A135259 A135260
Sequence in context: A118778 A108635 A071964 this_sequence A118697 A118695 A118693
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KEYWORD
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nonn
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AUTHOR
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Jonathan Vos Post (jvospost3(AT)gmail.com), Dec 01 2007
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EXTENSIONS
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Corrected and extended by R. J. Mathar (mathar(AT)strw.leidenuniv.nl), Jan 08 2008
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