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Search: id:A085929
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| A085929 |
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Smaller of two consecutive numbers with the same prime signature not occurring earlier. |
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+0
2
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| 2, 14, 44, 135, 230, 819, 2295, 2511, 5264, 7314, 8991, 11780, 21735, 23275, 29888, 37664, 41624, 156735, 223244, 257499, 378014, 458864, 477224, 916352, 1241954, 2808351, 3341624, 4122495, 4388175, 4402431, 5430375, 5475519, 6481475
(list; graph; listen)
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OFFSET
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0,1
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COMMENT
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The order of the exponents in the prime factorization is not significant (compare A091405).
Conjecture: (1) The sequence is infinite. (2) For every prime signature other than perfect powers, there exists a number k such that k+1 also has the same prime signature.
Up to at least 3*10^8, all numbers in this sequence have signatures with some prime to power 1 (for example, p^2*q^3 does not appear), casting some doubt on the second conjecture. - Joseph Myers (jsm(AT)polyomino.org.uk), Feb 24 2004
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EXAMPLE
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2 and 3 both are prime, 14 and 15 both are of the type p*q and 44 and 45 both are of the prime signature p^2*q. All prime signatures occur only once.
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CROSSREFS
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Cf. A025487, A091405.
Sequence in context: A108478 A075036 A091405 this_sequence A036659 A079937 A083102
Adjacent sequences: A085926 A085927 A085928 this_sequence A085930 A085931 A085932
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KEYWORD
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nonn
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AUTHOR
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Amarnath Murthy (amarnath_murthy(AT)yahoo.com), Jul 14 2003
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EXTENSIONS
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More terms from Joseph Myers (jsm(AT)polyomino.org.uk), Feb 24 2004
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