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A046413
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Numbers n such that the repunit of length n (11...11, with n 1's) has exactly 2 prime factors.
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8
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3, 4, 5, 7, 11, 17, 47, 59, 71, 139, 211, 251, 311, 347, 457, 461
(list; graph; refs; listen; history; internal format)
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OFFSET
| 1,1
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COMMENTS
| 347, 457, 461 and 701 are also terms. The only other possible terms up to 1000 are 263, 311, 509, 557, 617, 647 and 991; repunits of these lengths are known to be composite but the linked sources do not provide their factors. - Rick L. Shepherd (rshepherd2(AT)hotmail.com), Mar 11 2003
The Yousuke Koide reference now shows repunit of length 263 partially factored, no longer possible candidate for this sequence. - Ray Chandler (rayjchandler(AT)sbcglobal.net), Sep 06 2005
The term 263 has 3 prime factors, 617 has one prime factor and a large composite. For terms between 1000 to 2000, other possible terms are 1117, 1213, 1259, 1291, 1373, 1447, 1607, 1637, 1663, 1669, 1759, 1823, 1949, 1987, 2063 & 2087. [From Robert G. Wilson v (rgwv(AT)rgwv.com), Apr 26 2010]
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REFERENCES
| Clifford A. Pickover, A Passion for Mathematics, Wiley, 2005; see p. 60.
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LINKS
| P. De Geest, Repunits prime factors
Makoto Kamada, Factorizations of 11...11 (Repunit)
Yousuke KOIDE, Factorizations of Repunit Numbers.
Eric Weisstein's World of Mathematics, Repunit
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EXAMPLE
| a(n)=7 so 1111111 = 239*4649.
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CROSSREFS
| Cf. A000042, A004022 (the actual primes), A046053, A102782.
Sequence in context: A095880 A076497 A137950 * A120635 A113533 A023713
Adjacent sequences: A046410 A046411 A046412 * A046414 A046415 A046416
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KEYWORD
| nonn,base,changed
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AUTHOR
| Patrick De Geest (pdg(AT)worldofnumbers.com), Jul 15 1998.
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EXTENSIONS
| More terms from Rick L. Shepherd (rshepherd2(AT)hotmail.com), Mar 11 2003
a(13) - a(16) from Robert G. Wilson v (rgwv(AT)rgwv.com), Apr 26 2010
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