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Search: id:A004023
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| A004023 |
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Indices of prime "repunits": numbers n such that 11...111 = (10^n - 1)/9 is prime.
(Formerly M2114)
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68
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OFFSET
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1,1
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COMMENT
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The indices of primes with digital product (i.e. product of digits) equal to 1.
The larger terms may only correspond to probable primes.
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REFERENCES
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J. Brillhart et al., Factorizations of b^n +- 1. Contemporary Mathematics, Vol. 22, Amer. Math. Soc., Providence, RI, 2nd edition, 1985; and later supplements.
Harvey Dubner, New probable prime repunit R(49081), posting to Number Theory List (NMBRTHRY(AT)LISTSERV.NODAK.EDU) Sep 09, 1999.
Harvey Dubner, Repunit R49081 is a probable prime, Math. Comp., 71 (2001), 833-835.
H. C. Williams and Harvey Dubner, The primality of R1031, Math. Comp., 47(176), Oct 1986, 703-711.
Clifford A. Pickover, A Passion for Mathematics, Wiley, 2005; see p. 60.
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LINKS
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J. Brillhart et al., Factorizations of b^n +- 1, Contemporary Mathematics, Vol. 22, Amer. Math. Soc., Providence, RI, 3rd edition, 2002.
K. S. Brown's Mathpages, Seeking Prime Repunits
C. K. Caldwell, The Prime Glossary, Repunit
Patrick De Geest, Circular Primes
H. Dubner, Posting to Number Theory List : 3 April 2007
Makoto Kamada, Factorizations of 11...11 (Repunit).
H. Lifchitz, Mersenne and Fermat primes field
Andy Steward, Prime Generalized Repunits
S. S. Wagstaff, Jr., The Cunningham Project
E. Wegrzynowski, Nombres 1_[n] premiers
Eric Weisstein's World of Mathematics, Repunit
Eric Weisstein's World of Mathematics, Integer Sequence Primes
Index entries for primes involving repunits
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EXAMPLE
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2 appears because the 2-digit repunit 11 = eleven is prime. 19 appears because the 19-digit repunit 1111111111111111111 is prime.
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CROSSREFS
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See A004022 for the actual primes.
Cf. A055557, A002275.
Adjacent sequences: A004020 A004021 A004022 this_sequence A004024 A004025 A004026
Sequence in context: A037003 A105907 A018696 this_sequence A031030 A083689 A102617
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KEYWORD
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hard,nonn,nice
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AUTHOR
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njas
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EXTENSIONS
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49081 found by Harvey Dubner - posting to Number Theory List (NMBRTHRY(AT)LISTSERV.NODAK.EDU) Sep 09, 1999.
86453 found using pfgw (a faster version of PrimeForm) on Oct 26 2000 by Lew Baxter (ldenverb(AT)hotmail.com) - posting to Number Theory List (NMBRTHRY(AT)LISTSERV.NODAK.EDU), Oct 26, 2000.
a(8) = 109297 was apparently discovered independently by (in alphabetical order) Paul Bourdelais (paul.bourdelais(AT)gd-ais.com) and Harvey Dubner (harvey(AT)dubner.com) around Mar 26-28 2007.
A new probable prime repunit, R(270343), was found Jul 11 2007 by Maksym Voznyy (mvoznyy0526(AT)ROGERS.COM) and Anton Budnyy.
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