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Search: id:A160353
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| A160353 |
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Numbers of the form pqr, where p<q<r are odd primes such that r = +/-1 (mod pq). |
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+0
4
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| 435, 465, 861, 885, 903, 915, 1335, 1743, 2211, 2235, 2265, 2485, 2667, 2685, 2715, 3081, 3165, 3507, 3585, 3615, 4035, 4065, 4323, 4431, 4865, 4965, 5151, 5253, 5271, 5385, 5835, 5995, 6123, 6153, 6285, 6315, 6441, 6501, 6567, 6735, 7077, 7185, 7385
(list; graph; listen)
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OFFSET
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1,1
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COMMENT
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Kaplan (2007) has shown that this is a subsequence of A117223 (and thus of A160350; see there for the reference), i.e. the cyclotomic polynomial Phi[n] has coefficients in {0,1,-1} for indices n listed here.
This is a subsequence of A160352 which drops the requirement p>2.
See A160350 for further details and references.
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EXAMPLE
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a(1)=435=3*5*29 is the smallest product of odd primes p<q<r such that r is congruent to +/- 1 modulo the product of the smaller factors, p*q.
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PROGRAM
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(PARI) forstep( pqr=1, 9999, 2, my(f=factor(pqr)); #f~==3 & vecmax(f[, 2])==1 & abs((f[3, 1]+1)%(f[1, 1]*f[2, 1])-1)==1 & print1(pqr", "))
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CROSSREFS
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Sequence in context: A145318 A054987 A054905 this_sequence A124043 A084293 A088893
Adjacent sequences: A160350 A160351 A160352 this_sequence A160354 A160355 A160356
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KEYWORD
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nonn
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AUTHOR
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M. F. Hasler (MHasler(AT)univ-ag.fr), May 11 2009
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