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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
3, 4, 5, 7, 11, 17, 47, 59, 71, 139, 211, 251, 311, 347, 457, 461 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,1

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, Mar 11 2003

The Yousuke Koide reference now shows repunit of length 263 partially factored, no longer possible candidate for this sequence. - Ray Chandler, 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. - Robert G. Wilson v, Apr 26 2010

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

REFERENCES

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

LINKS

Table of n, a(n) for n=1..16.

P. De Geest, Repunits prime factors

Makoto Kamada, Factorizations of 11...11 (Repunit).

Yousuke Kiode, Factorizations of Repunit Numbers.

Eric Weisstein's World of Mathematics, Repunit

EXAMPLE

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

CROSSREFS

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

Sequence in context: A095880 A076497 A137950 * A285224 A120635 A023713

Adjacent sequences:  A046410 A046411 A046412 * A046414 A046415 A046416

KEYWORD

nonn,base

AUTHOR

Patrick De Geest, Jul 15 1998

EXTENSIONS

More terms from Rick L. Shepherd, Mar 11 2003

a(13)-a(16) from Robert G. Wilson v, Apr 26 2010

STATUS

approved

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Last modified September 20 12:31 EDT 2017. Contains 292271 sequences.