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Search: id:A072875
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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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+0
8
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| 2, 3, 61, 193, 15121, 838561, 807905281, 19896463921, 3059220303001, 3931520917431241
(list; graph; listen)
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OFFSET
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1,1
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COMMENT
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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 http://www.primepuzzles.net/puzzles/puzz_425.htm. - sent by amd64(AT)vipmail.hu, Dec 21 2007
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REFERENCES
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J.-M. De Koninck, Ces nombres qui nous fascinent, Entry 61, p. 22, Ellipses, Paris 2008.
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LINKS
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alt.math.recreational thread, Consecutive numbers with counting prime factors
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EXAMPLE
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a(3)=61 because 61(prime), 62(=2*31), 63(=3*3*7) has exactly 1, 2, 3 prime factors 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
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Cf. A001222, A093552, A093550, A086560, A124592.
Sequence in context: A112098 A085326 A062308 this_sequence A093551 A061452 A037426
Adjacent sequences: A072872 A072873 A072874 this_sequence A072876 A072877 A072878
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KEYWORD
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hard,nice,nonn,more
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AUTHOR
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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
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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 njas, Jan 26 2007
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