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A099011 Pell pseudoprimes: odd composite numbers n such that P(n)-Kronecker(2,n) is divisible by n. 2
169, 385, 741, 961, 1121, 2001, 3827, 4879, 5719, 6215, 6265, 6441, 6479, 6601, 7055, 7801, 8119, 9799, 10945, 11395, 13067, 13079, 13601, 15841, 18241, 19097, 20833, 20951, 24727, 27839, 27971, 29183, 29953, 31417, 31535, 34561, 35459, 37345 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,1

COMMENTS

Here P(n) are the Pell numbers (A000129), defined by P(0)=0, P(1)=1, P(x) = 2*P(x-1) + P(x-2) and Kronecker(2,n) is equal to 1 if n is congruent to +-1 mod 8 and equal to -1 if n is congruent to +-3 mod 8.

LINKS

Ralf Stephan, Table of n, a(n) for n = 1..200 (Pell pseudoprimes up to 1000000)

Dana Jacobsen, Pseudoprime Statistics, Tables, and Data (includes terms to 5e12)

EXAMPLE

169 is a Pell pseudoprime because P(169)-Kronecker(2,169) is divisible by 169.

PROG

(Perl)

use Math::Prime::Util qw/:all/;

my($U, $V);

foroddcomposites {

  ($U, $V) = lucas_sequence($_, 2, -1, $_);

  $U = ($U - kronecker(2, $_)) % $_;

  print "$_\n" if $U == 0;

} 1e11;   # Dana Jacobsen, Sep 13 2014

CROSSREFS

Cf. A000129.

Sequence in context: A287391 A296304 A156159 * A112076 A305055 A069645

Adjacent sequences:  A099008 A099009 A099010 * A099012 A099013 A099014

KEYWORD

nonn

AUTHOR

Jack Brennen, Nov 13 2004

STATUS

approved

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Last modified May 21 00:41 EDT 2019. Contains 323427 sequences. (Running on oeis4.)