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A182381
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Carmichael numbers divisible by 17 and 29.
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1
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2465, 278545, 13696033, 75151441, 93869665, 169570801, 490099681, 612347905, 707926801, 744866305, 1190790721, 1321983937, 1913016001, 2159003281, 2176838049, 2232385345, 2353639681, 3880251649, 4059151489, 4314912001, 5204110465, 8355729313, 8548543585, 9584174881, 10054063041, 10933377841
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OFFSET
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1,1
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COMMENTS
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Conjecture: Any Carmichael number C divisible by 17 and 29 can be written as C = 952*n + 561; checked up to the Carmichael number 105823343809.
Note: the number 561 is the first Carmichael number and the number 952 comes from the following interesting relation: 952^2 = 1105^2 - 561^2 (where 1105 is the second Carmichael number).
The conjecture follows from Korselt's criterion. More is true: a(n) = 2465 mod 55216. - Charles R Greathouse IV, Oct 02 2012
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LINKS
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PROG
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(PARI) Korselt(n)=my(f=factor(n)); for(i=1, #f[, 1], if(f[i, 2]>1||(n-1)%(f[i, 1]-1), return(0))); 1
list(lim)=my(v=List()); forstep(n=2465, lim, 55216, if(Korselt(n), listput(v, n))); Vec(v) \\ Charles R Greathouse IV, Jun 30 2017
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CROSSREFS
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KEYWORD
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nonn
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AUTHOR
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EXTENSIONS
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STATUS
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approved
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