cp's OEIS Frontend

This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.

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

This page as a plain text file.
%I A227905 #40 Jun 28 2019 14:42:43
%S A227905 741751,1024651,5481451,31150351,109437751,139952671,178482151,
%T A227905 284301751,383425351,395044651,407282851,417027451,498706651,
%U A227905 582799951,612816751,620072251,652969351,738820351,977755351,1126587151,1204176751,1397357851,1588247851,1789167931
%N A227905 Numbers of the form 4k+3 (A004767) that are Lucas pseudoprimes and Fermat pseudoprimes to base 2 (intersection of A005845 and A001567).
%C A227905 This sequence uses the Bruckman definition of "Lucas pseudoprime". There are 400,114 examples less than 2^64. - _Dana Jacobsen_, Jan 07 2015
%H A227905 Amiram Eldar, <a href="/A227905/b227905.txt">Table of n, a(n) for n = 1..10000</a>
%H A227905 J. M. Grau, A. M. Oller-Marcen, M. Rodríguez, D. Sadornil, <a href="http://arxiv.org/abs/1401.4708">Fermat test with gaussian base and Gaussian pseudoprimes</a>, arXiv preprint arXiv:1401.4708 [math.NT], 2014.
%H A227905 W. Galway, <a href="http://www.cecm.sfu.ca/Pseudoprimes/index-2-to-64.html">Tables of pseudoprimes and related data</a> [Includes a file with base-2 Fermat pseudoprimes up to 2^64.]
%t A227905 Select[4*Range[8000000]+3, CompositeQ[#] && PowerMod[2, (# - 1), # ] == 1 && Divisible[LucasL[#]-1, #] &] (* _Amiram Eldar_, Jun 27 2019 *)
%o A227905 # Using the Feitsma/Galway database from the links:
%o A227905 (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
%o A227905 (Perl) perl -Mntheory=:all -E 'foroddcomposites { say if $_%4 == 3 && ispseudoprime($_,2) && (lucas_sequence($_,1,-1,$_))[1] == 1 } 1e14'  # _Dana Jacobsen_, Jan 10 2015
%Y A227905 Cf. A004767 (4n+3).
%Y A227905 Cf. A001567 (Fermat pseudoprimes to base 2), A005845 (Lucas pseudoprimes).
%K A227905 nonn
%O A227905 1,1
%A A227905 _José María Grau Ribas_, Oct 12 2013
%E A227905 More terms from _Dana Jacobsen_, Jan 07 2015
%E A227905 a(16)-a(24) from _Amiram Eldar_, Jun 27 2019