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Fibonacci(n-J(n,5)) mod n^2, where J is the Jacobi symbol.
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%I #20 Sep 08 2022 08:45:23

%S 0,2,3,2,5,5,21,34,21,55,55,89,39,37,160,98,272,293,57,365,150,101,

%T 345,433,25,665,696,709,754,440,775,994,883,1090,765,1241,481,230,

%U 1511,1355,1599,257,1677,805,20,1382,752,289,2275,1525,1414,821,1484

%N Fibonacci(n-J(n,5)) mod n^2, where J is the Jacobi symbol.

%C a(n) == 0 for n > 1 iff either n is a Wall-Sun-Sun prime (when n is prime) or a 'Wall-Sun-Sun pseudoprime' (when n is composite). The numbers meeting the second criterion are those composites where the congruence in A241505 is satisfied modulo n^2. No members are known from either of those two sets of numbers. - _Felix Fröhlich_, May 15 2015

%H T. D. Noe, <a href="/A113649/b113649.txt">Table of n, a(n) for n = 1..10000</a>

%H Eric Weisstein's World of Mathematics, <a href="http://mathworld.wolfram.com/Wall-Sun-SunPrime.html">Wall-Sun-Sun Prime</a>

%o (PARI) a(n)=lift(Mod([1, 1; 1, 0]^(n-kronecker(n, 5)), n^2)[1, 2]) \\ _Charles R Greathouse IV_, Oct 31 2011

%o (PARI) a(n) = fibonacci(n-kronecker(n,5)) % n^2 \\ _Jeppe Stig Nielsen_, Jul 22 2014

%o (Magma) [Fibonacci(n-(KroneckerSymbol(n,5))) mod n^2: n in [1..70]]; // _Vincenzo Librandi_, May 16 2015

%Y Cf. A113650.

%K nonn

%O 1,2

%A _Eric W. Weisstein_, Nov 03 2005