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A046413 Numbers n such that the repunit of length n (11...11, with n 1's) has exactly 2 prime factors. 10

%I

%S 3,4,5,7,11,17,47,59,71,139,211,251,311,347,457,461

%N Numbers n such that the repunit of length n (11...11, with n 1's) has exactly 2 prime factors.

%C 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_, Mar 11 2003

%C The Yousuke Koide reference now shows repunit of length 263 partially factored, no longer possible candidate for this sequence. - _Ray Chandler_, Sep 06 2005

%C 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. - _Robert G. Wilson v_, Apr 26 2010

%C All terms are either primes or squares of primes in A004023. In particular, the only composite below a million is 4. - _Charles R Greathouse IV_, Nov 21 2014

%D Clifford A. Pickover, A Passion for Mathematics, Wiley, 2005; see p. 60.

%H P. De Geest, <a href="http://www.worldofnumbers.com/repunits.htm">Repunits prime factors</a>

%H Makoto Kamada, <a href="https://stdkmd.net/nrr/repunit">Factorizations of 11...11 (Repunit)</a>.

%H Yousuke Kiode, <a href="http://www.h4.dion.ne.jp/~rep">Factorizations of Repunit Numbers</a>.

%H Eric Weisstein's World of Mathematics, <a href="http://mathworld.wolfram.com/Repunit.html">Repunit</a>

%e a(n)=7 so 1111111 = 239*4649.

%Y Cf. A000042, A004022 (the actual primes), A046053, A102782.

%K nonn,base

%O 1,1

%A _Patrick De Geest_, Jul 15 1998

%E More terms from _Rick L. Shepherd_, Mar 11 2003

%E a(13)-a(16) from _Robert G. Wilson v_, Apr 26 2010

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Last modified June 25 14:43 EDT 2019. Contains 324352 sequences. (Running on oeis4.)