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A083737
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Pseudoprimes to bases 2, 3 and 5.
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9
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1729, 2821, 6601, 8911, 15841, 29341, 41041, 46657, 52633, 63973, 75361, 101101, 115921, 126217, 162401, 172081, 188461, 252601, 294409, 314821, 334153, 340561, 399001, 410041, 488881, 512461, 530881, 552721, 658801, 670033, 721801, 748657
(list; graph; refs; listen; history; internal format)
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OFFSET
| 1,1
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COMMENTS
| a(n) = n-th positive integer k(>1) such that 2^(k-1) == 1 (mod k), 3^(k-1) == 1 (mod k) and 5^(k-1) == 1 (mod k)
See A153580 for numbers k > 1 such that 2^k-2, 3^k-3 and 5^k-5 are all divible by k but k is not a Carmichael number (A002997).
Note that a(1)=1729 is the Hardy-Ramanujan number. [From Omar E. Pol (info(AT)polprimos.com), Jan 18 2009]
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LINKS
| R. J. Mathar, Table of n, a(n) for n=1..102
J. Bernheiden, Pseudoprimes (Text in German)
F. Richman, Primality testing with Fermat's little theorem
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EXAMPLE
| a(1)=1729 since it is the first number such that 2^(k-1) == 1 (mod k), 3^(k-1) == 1 (mod k) and 5^(k-1) == 1 (mod k).
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MATHEMATICA
| Select[ Range[838200], !PrimeQ[ # ] && PowerMod[2, # - 1, # ] == 1 && PowerMod[3, 1 - 1, # ] == 1 && PowerMod[5, # - 1, # ] == 1 & ]
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CROSSREFS
| Proper subset of A052155. Cf. A153580, A002997.
Cf. A001235, A011541. [From Omar E. Pol (info(AT)polprimos.com), Jan 18 2009]
Sequence in context: A033181 A198775 A154729 * A138129 A001235 A018850
Adjacent sequences: A083734 A083735 A083736 * A083738 A083739 A083740
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KEYWORD
| easy,nonn
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AUTHOR
| Serhat Sevki Dincer (sevki(AT)ug.bilkent.edu.tr), May 05 2003
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EXTENSIONS
| Edited by Robert G. Wilson v (rgwv(AT)rgwv.com), May 06 2003
Edited by N. J. A. Sloane (njas(AT)research.att.com), Jan 14 2009
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