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Search: id:A026416
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| A026416 |
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A 2-way classification of integers: a(1) = 1, a(2) = 2 and for n > 2, a(n) is the smallest number not of the form a(i)*a(j) for 1 <= i < j < n. |
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+0
9
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| 1, 2, 3, 4, 5, 7, 9, 11, 13, 16, 17, 19, 23, 24, 25, 29, 30, 31, 37, 40, 41, 42, 43, 47, 49, 53, 54, 56, 59, 61, 66, 67, 70, 71, 73, 78, 79, 81, 83, 88, 89, 97, 101, 102, 103, 104, 105, 107, 109, 110, 113, 114, 121, 127, 128, 130, 131, 135, 136, 137, 138, 139, 149, 151, 152, 154, 157, 163, 165, 167, 169, 170, 173, 174, 179, 180, 181, 182, 184, 186, 189, 190, 191, 192, 193, 195, 197, 199, 211, 222, 223, 227, 229, 230, 231, 232, 233, 238, 239, 240, 241
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OFFSET
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1,2
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COMMENT
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An equivalent definition is: a(1) = 1, a(2) = 2; and for n > 2, a(n) = least positive integer > a(n-1) and not of the form a(i)*a(j) for 1 <= i < j < n.
A variant of A000028, differing only in the inclusion of 1.
This has a simpler definition than A000028, but the resulting pair lacks the crucial property of the A000028/A000379 pair (see the comment in A000028). - N. J. A. Sloane (njas(AT)research.att.com), Sep 28 2007
Contains (for example) 180, so is different from A123193. - Max Alekseyev, Sep 20 2007
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EXAMPLE
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a(8) is not 10 because we already have 10 = 2*5. Of course all primes appear. 16 appears because 16 is not a product of earlier terms.
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CROSSREFS
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Complement of A131181. Cf. A000028.
Cf. A066724, A026477, A050376, A084400.
Sequence in context: A005706 A064175 A000028 this_sequence A123193 A066724 A079851
Adjacent sequences: A026413 A026414 A026415 this_sequence A026417 A026418 A026419
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KEYWORD
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nonn,easy
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AUTHOR
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Clark Kimberling (ck6(AT)evansville.edu)
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EXTENSIONS
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More terms from Max Alekseyev (maxale(AT)gmail.com), Sep 23 2007
Edited by N. J. A. Sloane (njas(AT)research.att.com), Jul 13 2008 at the suggestion of R. J. Mathar and Max Alekseyev
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