A298945 a(n) = F_{c-(5/c)} mod c^2, where c is the n-th composite number, F_i = A000045(i) and (5/c) is the Kronecker symbol.

2, 5, 34, 21, 55, 89, 37, 160, 98, 293, 365, 150, 101, 433, 25, 665, 696, 709, 440, 994, 883, 1090, 765, 1241, 230, 1511, 1355, 257, 805, 20, 1382, 289, 2275, 1525, 1414, 821, 1373, 1820, 685, 1504, 2177, 720, 3102, 1302, 1250, 190, 2425, 2178, 2832, 3935

Offset

1,1

Comments

Composites c where a(n) = 0 could be called "Wall-Sun-Sun pseudoprimes" or "Fibonacci-Wieferich pseudoprimes". Do any such composites exist?

Any such c would have to be a term of A241505.

Links

Robert Israel, Table of n, a(n) for n = 1..10000

Maple

N:= 100: # to get a(1)..a(N)
count:= 0: R:= NULL:
for n from 4 while count < N do
if not isprime(n) then
  count:= count+1;
  R:= R, combinat:-fibonacci(n - numtheory:-jacobi(5, n)) mod n^2;
fi
od:
R; # Robert Israel, Feb 02 2018

Mathematica

composite[n_Integer] := FixedPoint[n + PrimePi@ # + 1 &, n + PrimePi@ n + 1] ; Array[With[{c = composite@ #}, Mod[Fibonacci[c - KroneckerSymbol[5, c]], c^2]] &, 50] (* Michael De Vlieger, Jan 31 2018, composite function by Robert G. Wilson v at A066277 *)

Prog

(PARI) forcomposite(c=1, 200, print1(lift(Mod(fibonacci(c-kronecker(5, c)), c^2)), ", "))

Crossrefs

Cf. A000045, A241505, A298944, A298946.

Sequence in context: A333738 A114793 A254429 * A027303 A357446 A371615

Adjacent sequences: A298942 A298943 A298944 * A298946 A298947 A298948

Keyword

nonn

Author

Felix Fröhlich, Jan 30 2018

Status

approved