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 A099011 Pell pseudoprimes: odd composite numbers n such that P(n)-Kronecker(2,n) is divisible by n. 7
 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 Amiram Eldar, Table of n, a(n) for n = 1..10000 (from Dana Jacobsen's site, terms 1..200 from Ralf Stephan) Antonio J. Di Scala, Nadir Murru, Carlo Sanna, Lucas pseudoprimes and the Pell conic, arXiv:2001.00353 [math.NT], 2020. 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. MATHEMATICA pell[0] = 0; pell[1] = 1; pell[n_] := pell[n] = 2*pell[n - 1] + pell[n - 2]; pellpspQ[n_] := OddQ[n] && CompositeQ[n] && Divisible[pell[n] - JacobiSymbol[2, n], n]; Select[Range[40000], pellpspQ] (* Amiram Eldar, Nov 22 2019 *) 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: A325421 A296304 A156159 * A330276 A351337 A327652 Adjacent sequences: A099008 A099009 A099010 * A099012 A099013 A099014 KEYWORD nonn AUTHOR Jack Brennen, Nov 13 2004 STATUS approved

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Last modified June 4 16:30 EDT 2023. Contains 363128 sequences. (Running on oeis4.)