A351989 Fibonacci(p-J(p,5)) mod p^3, where p is the n-th prime and J is the Jacobi symbol.
2, 3, 5, 21, 55, 377, 2584, 2584, 9867, 754, 27683, 34706, 55391, 77486, 2961, 49237, 178121, 151768, 269809, 180340, 137459, 440741, 304859, 634125, 3589, 224018, 925249, 689508, 276097, 389850, 1566164, 488892, 101791, 731140, 1838362, 3406409, 31557, 2311014, 3158805, 4571698, 2914836, 3267050, 1294789, 6599056, 7246251, 159399
Offset: 1
Crossrefs
Cf. A113650.
Programs
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Mathematica
a[n_]:= Mod[Fibonacci[(n-JacobiSymbol[n, 5])], Power[n, 3]]; Table[a[Prime[n]], {n, 50}] -
PARI
a(n) = my(p=prime(n)); lift(Mod([1, 1; 1, 0]^(p-kronecker(p, 5)), p^3)[1, 2]); \\ Michel Marcus, Feb 28 2022
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Python
from sympy import prime, fibonacci from sympy.ntheory import jacobi_symbol def A351989(n): return fibonacci((p := prime(n))-jacobi_symbol(p,5)) % p**3 # Chai Wah Wu, Feb 28 2022
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Sage
p = 1 while p < 200: print(fibonacci(p-jacobi_symbol(p,5))%pow(p,3), end=', ') p = next_prime(p)
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