A395295 a(n) = L(1,p)-L(-1,p)-L(0,p) where p is the n-th odd prime and L(j,p) is the number of i with 0<=i<A001175(p) for which the Legendre symbol (A000045(i)/p)=j.

-2, -4, -2, 0, -4, 12, -2, -2, 0, 0, -4, 8, -2, -2, -4, -2, -4, -2, 0, 28, -2, -2, 20, -20, -2, -2, -2, -4, 4, -2, 0, -20, 4, -4, -2, -4, -2, -2, -4, -2, -2, 0, 44, -4, 6, 8, -2, -2, 0, 12, -2, -32, 0, -68, -2, -4, 0, -4, 0, -2, -4, -2, 0, 44, -4, 10, 60, -2, 0, 52, -2, -2, -4, -2, -2, -4, -4, -4, 4, -2, -4, 0

Offset

1,1

Links

Jason D. Andoyo, Table of n, a(n) for n = 1..9591

Jason D. Andoyo, (a,b)-Fibonacci-Legendre Cordial Graphs and k-Pisano-Legendre Primes, Annals of Communications in Mathematics, 9(1), Article no. 11.

Prog

(Python)
from sympy import legendre_symbol, primerange
def kval(p, in1, in2):
    L, a, b, in1, in2 = [], in1, in2, in1%p, in2%p
    while True:
        L.append(legendre_symbol(a, p))
        a, b = b, (a + b)%p
        if (a, b) == (in1, in2): break
    return L.count(1) - L.count(-1) - L.count(0)
print([kval(p, 0, 1) for p in primerange(3, 500)])
(PARI) fibmod(n, m) = ((Mod([1, 1; 1, 0], m))^n)[1, 2];
isok(k, n) = (fibmod(k, n) == 0) && (fibmod(k+1, n) == 1);
pp(n) = my(k=1); while(!isok(k, n), k++); k; \\ A001175
L(k, p) = sum(i=0, pp(p)-1, kronecker(fibonacci(i), p) == k);
a(n) = my(p=prime(n+1)); L(1, p)-L(-1, p)-L(0, p); \\ Michel Marcus, Apr 20 2026

Crossrefs

Cf. A394870, A000045, A001175, A000040, A065091.

Sequence in context: A258711 A127278 A378010 * A356165 A366589 A335764

Adjacent sequences: A395292 A395293 A395294 * A395296 A395297 A395298

Keyword

sign

Author

Jason D. Andoyo, Apr 18 2026

Status

approved