A227905 Numbers of the form 4k+3 (A004767) that are Lucas pseudoprimes and Fermat pseudoprimes to base 2 (intersection of A005845 and A001567).

741751, 1024651, 5481451, 31150351, 109437751, 139952671, 178482151, 284301751, 383425351, 395044651, 407282851, 417027451, 498706651, 582799951, 612816751, 620072251, 652969351, 738820351, 977755351, 1126587151, 1204176751, 1397357851, 1588247851, 1789167931

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

Amiram Eldar, Table of n, a(n) for n = 1..10000

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

Adjacent sequences: A227902 A227903 A227904 * A227906 A227907 A227908

Keyword

nonn

Author

José María Grau Ribas, Oct 12 2013

Extensions

More terms from Dana Jacobsen, Jan 07 2015

a(16)-a(24) from Amiram Eldar, Jun 27 2019

Status

approved