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A227905 Numbers of the form 4k+3 (A004767) that are Lucas pseudoprimes and Fermat pseudoprimes to base 2 (intersection of A005845 and A001567). 2
741751, 1024651, 5481451, 31150351, 109437751, 139952671, 178482151, 284301751, 383425351, 395044651, 407282851, 417027451, 498706651, 582799951, 612816751, 620072251, 652969351, 738820351, 977755351, 1126587151, 1204176751, 1397357851, 1588247851, 1789167931 (list; graph; refs; listen; history; text; internal format)
OFFSET
1,1
COMMENTS
This sequence uses the Bruckman definition of "Lucas pseudoprime". There are 400,114 examples less than 2^64. - Dana Jacobsen, Jan 07 2015
LINKS
J. M. Grau, A. M. Oller-Marcen, M. Rodríguez, D. Sadornil, Fermat test with gaussian base and Gaussian pseudoprimes, arXiv preprint arXiv:1401.4708 [math.NT], 2014.
W. Galway, Tables of pseudoprimes and related data [Includes a file with base-2 Fermat pseudoprimes up to 2^64.]
MATHEMATICA
Select[4*Range[8000000]+3, CompositeQ[#] && PowerMod[2, (# - 1), # ] == 1 && Divisible[LucasL[#]-1, #] &] (* Amiram Eldar, Jun 27 2019 *)
PROG
# 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
CROSSREFS
Cf. A004767 (4n+3).
Cf. A001567 (Fermat pseudoprimes to base 2), A005845 (Lucas pseudoprimes).
Sequence in context: A184504 A249317 A251487 * A282407 A147707 A133183
KEYWORD
nonn
AUTHOR
EXTENSIONS
More terms from Dana Jacobsen, Jan 07 2015
a(16)-a(24) from Amiram Eldar, Jun 27 2019
STATUS
approved

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Last modified February 29 14:25 EST 2024. Contains 370425 sequences. (Running on oeis4.)