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Search: id:A101186
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| A101186 |
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Values of k for which 7m+1, 8m+1 and 11m+1 are prime, with m=1848k+942. |
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+0
3
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| 13, 123, 218, 223, 278, 411, 513, 551, 588, 733, 743, 796, 856, 928, 1168, 1226, 1263, 1401, 1533, 1976, 1981, 2013, 2096, 2138, 2241, 2376, 2556, 2676, 2703, 3626, 3703, 3718, 3971, 4008, 4121, 4138, 4163, 4188, 4211, 4313, 4423, 4653, 4656, 4901, 5018
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OFFSET
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1,1
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COMMENT
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The number (7m+1)(8m+1)(11m+1) is a 3-factor Carmichael number if and only if m is equal to 1848k+942 with k in this sequence. The sequence includes the value k=10^329-4624879 which yields a 1000-digit Carmichael number with three prime factors of 334 digits each. Other Carmichael numbers of the same form would necessarily have 4 prime factors or more; the smallest such example is 3664585=127*(7*29)*199, for m=18.
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LINKS
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G. P. Michon, Generic Carmichael Numbers.
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EXAMPLE
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a(1)=13 because k=13 corresponds to m=24966, which yields a product of three primes (7m+1)(8m+1)(11m+1) equal to the Carmichael number 9585921133193329 (among all Carmichael numbers with 16 digits or less, as first listed by Richard G.E. Pinch, this one features the largest "least prime factor").
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CROSSREFS
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Cf. A002997 (Carmichael numbers). A046025.
Sequence in context: A096053 A033470 A016230 this_sequence A115204 A016277 A134550
Adjacent sequences: A101183 A101184 A101185 this_sequence A101187 A101188 A101189
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KEYWORD
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nonn
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AUTHOR
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Gerard P. Michon (g.michon(AT)att.net), Dec 03 2004
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