A051831 -id:A051831 - cp's OEIS frontend

A051830 a(n) = Fibonacci(p(n)+1) mod p(n), where p(n) is the n-th prime.

0, 0, 3, 0, 1, 0, 0, 1, 0, 1, 1, 0, 1, 0, 0, 0, 1, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 0, 1, 0, 0, 1, 0, 1, 1, 1, 0, 0, 0, 0, 1, 1, 1, 0, 0, 1, 1, 0, 0, 1, 0, 1, 1, 1, 0, 0, 1, 1, 0, 1, 0, 0, 0, 1, 0, 0, 1, 0, 0, 1, 0, 1, 0, 0, 1, 0, 1, 0, 1, 1, 1, 1, 1, 0, 1, 0, 1, 0, 1, 0, 0, 1, 0, 1, 1, 0, 1, 1, 0, 1, 0, 0, 0, 1, 1

Offset: 1

Jud McCranie, Dec 11 1999

nonn

Terms are 1 when p(n) == 1 or 4 (mod 5) and 0 when p(n) == 2 or 3 (mod 5).

			p(3) = 5, so a(3) = Fibonacci(5+1) mod 5 = 3.

Cf. A000040, A000045, A003631, A045468, A051834, A051831.

Table[Mod[Fibonacci[n+1],n],{n,Prime[Range[110]]}] (* Harvey P. Dale, Nov 27 2015 *)

a(n) = max(0, Legendre(5,prime(n))) for n >= 4, where Legendre is the Legendre symbol. - Haifeng Xu, Jan 31 2025

A236395 a(n) = Fibonacci(p) mod p^2, where p = prime(n).

Original entry on oeis.org

1, 2, 5, 13, 89, 64, 152, 210, 91, 378, 869, 443, 1641, 85, 1832, 2066, 296, 1465, 2009, 4474, 3211, 5057, 2572, 4184, 2909, 10000, 9475, 10164, 1418, 9378, 7238, 4193, 14795, 17793, 8941, 4531, 21194, 13528, 24214, 18683, 15574, 28237, 8978, 15632, 5515, 20299, 11817, 24529, 34049, 2062, 23765, 29159, 21932, 31376, 65791, 20776, 43848, 27101, 29638

Offset: 1

N. J. A. Sloane, Jan 28 2014

nonn

Alois P. Heinz, Table of n, a(n) for n = 1..20000

Cf. A030426, A051831, A132634.

p:= (M, n, k)-> map(x-> x mod k, `if`(n=0, <<1|0>, <0|1>>,
          `if`(n::even, p(M, n/2, k)^2, p(M, n-1, k).M))):
a:= n-> (q-> p(<<0|1>, <1|1>>, q, q^2)[1, 2])(ithprime(n)):
seq(a(n), n=1..80);  # Alois P. Heinz, Oct 10 2015

a(n) = my(p = prime(n)); fibonacci(p) % p^2; \\ Michel Marcus, Jan 29 2014

A051834 Fibonacci(Pn-1) mod Pn, where Pn is the n-th prime.

Original entry on oeis.org

1, 1, 3, 1, 0, 1, 1, 0, 1, 0, 0, 1, 0, 1, 1, 1, 0, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 1, 0, 1, 1, 0, 1, 0, 0, 0, 1, 1, 1, 1, 0, 0, 0, 1, 1, 0, 0, 1, 1, 0, 1, 0, 0, 0, 1, 1, 0, 0, 1, 0, 1, 1, 1, 0, 1, 1, 0, 1, 1, 0, 1, 0, 1, 1, 0, 1, 0, 1, 0, 0, 0, 0, 0, 1, 0, 1, 0, 1, 0, 1, 1, 0, 1, 0, 0, 1, 0, 0, 1, 0, 1, 1, 1

Offset: 1

Jud McCranie, Dec 11 1999

nonn

Terms are 0 when Pn == 1 or 4 mod 5, terms are 1 when Pn == 2 or 3 mod 5.

			P3=5, Fibonacci(5-1)=3 mod 5.

Cf. A000045, A003631, A045468, A051830, A051831.

cp's OEIS Frontend

A051830 a(n) = Fibonacci(p(n)+1) mod p(n), where p(n) is the n-th prime.

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A236395 a(n) = Fibonacci(p) mod p^2, where p = prime(n).

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A051834 Fibonacci(Pn-1) mod Pn, where Pn is the n-th prime.

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