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A072875
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Smallest start for a run of n consecutive numbers of which the i-th has exactly i prime factors.
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9
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OFFSET
| 1,1
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COMMENTS
| By definition each term of this sequence is prime.
Download search program (see alt.math.recreational thread) if you want to help search for the next term!
a(11) <= 1452591346605212407096281241 (Frederick Schneider), see primepuzzles link. - sent by amd64(AT)vipmail.hu, Dec 21 2007
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REFERENCES
| J.-M. De Koninck, Ces nombres qui nous fascinent, Entry 61, p. 22, Ellipses, Paris 2008.
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LINKS
| alt.math.recreational thread, Consecutive numbers with counting prime factors
J. M. Bergot, Puzzle 425. Consecutive numbers, increasing quantity of prime factors
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EXAMPLE
| a(3)=61 because 61(prime), 62(=2*31), 63(=3*3*7) have exactly 1, 2, 3 prime factors respectively, and this is the smallest solution
a(6)=807905281: 807905281 is prime; 807905281+1=2*403952641;
807905281+2=3*15733*17117; 807905281+3=2*2*1871*107951;
807905281+4=5*11*43*211*1619; 807905281+5=2*3*3*3*37*404357;
807905281+6=7*7*7*7*29*41*283; 807905281 is the smallest number m such that m+k is product of k+1 primes for k=0,1,2,3,4,5& 6.
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CROSSREFS
| Cf. A001222, A093552, A093550, A086560, A124592.
a(1) = A000040(1), a(2) = A005383(1), a(3) = A112998(1), a(4) = A113000(1), a(5) = A113008(1), a(6) = A113150(1)
Sequence in context: A144545 A085326 A062308 * A093551 A173915 A061452
Adjacent sequences: A072872 A072873 A072874 * A072876 A072877 A072878
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KEYWORD
| hard,nice,nonn,more
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AUTHOR
| Rick L. Shepherd (rshepherd2(AT)hotmail.com), Jun 30, 2002 and Jens Kruse Andersen (jens.k.a(AT)get2net.dk), Jul 28, 2002
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EXTENSIONS
| a(7) found by Mark W. Lewis. a(8) and a(9) found by Jens Kruse Andersen.
a(10) found by J. K. A. Probably a(11)>10^20. Aug 24, 2002
Entry revised by N. J. A. Sloane (njas(AT)research.att.com), Jan 26 2007
Cross-references and editing by Charles R Greathouse IV (charles.greathouse(AT)case.edu), Apr 20 2010
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