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A227905
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Numbers of the form 4k+3 (A004767) that are Lucas pseudoprimes and Fermat pseudoprimes to base 2 (intersection of A005845 and A001567).
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1
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741751, 1024651, 5481451, 31150351, 109437751, 139952671, 178482151, 284301751, 383425351, 395044651, 407282851, 417027451, 498706651, 582799951, 612816751
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OFFSET
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1,1
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COMMENTS
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This sequence uses the Bruckman definition of "Lucas pseudoprime". There are 400,114 examples less than 2^64. - Dana Jacobsen, Jan 07 2015
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LINKS
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Table of n, a(n) for n=1..15.
J. M. Grau, A. M. Oller-Marcen, M. Rodríguez, D. Sadornil, Fermat test with gaussian base and Gaussian pseudoprimes, arXiv preprint arXiv:1401.4708, 2014
W. Galway, Tables of pseudoprimes and related data [Includes a file with base-2 Fermat pseudoprimes up to 2^64.]
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PROG
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# Using the Feitsma/Galway database from the links:
(Perl) perl -Mntheory=:all -nE 'chomp; say if ($_%4)==3 && (lucas_sequence($_, 1, -1, $_))[1] == 1' psps-below-2-to-64.txt # Dana Jacobsen, Jan 07 2015
(Perl) perl -Mntheory=:all -E 'foroddcomposites { say if $_%4 == 3 && ispseudoprime($_, 2) && (lucas_sequence($_, 1, -1, $_))[1] == 1 } 1e14' # Dana Jacobsen, Jan 10 2015
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CROSSREFS
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Cf. A004767 (4n+3).
Cf. A001567 (Fermat pseudoprimes to base 2), A005845 (Lucas pseudoprimes).
Sequence in context: A184504 A249317 A251487 * A282407 A147707 A133183
Adjacent sequences: A227902 A227903 A227904 * A227906 A227907 A227908
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KEYWORD
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nonn,more
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AUTHOR
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José María Grau Ribas, Oct 12 2013
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EXTENSIONS
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More terms from Dana Jacobsen, Jan 07 2015
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STATUS
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approved
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