A116514 a(1) = 1; thereafter a(n) = (p - (5|p)) divided by the smallest m such that p divides Fibonacci(m), where p is the n-th prime and (5|p) is the Legendre symbol.

1, 1, 1, 1, 1, 2, 2, 1, 1, 2, 1, 2, 2, 1, 3, 2, 1, 4, 1, 1, 2, 1, 1, 8, 2, 2, 1, 3, 4, 6, 1, 1, 2, 3, 4, 3, 2, 1, 1, 2, 1, 2, 1, 2, 2, 9, 5, 1, 1, 2, 18, 1, 2, 1, 2, 3, 4, 1, 2, 10, 1, 2, 7, 1, 2, 2, 3, 2, 3, 2, 6, 1, 1, 2, 1, 1, 4, 2, 4, 2, 1, 20, 1, 2, 1, 1, 2, 2, 10, 1, 1, 1, 1, 1, 1, 1, 2, 20, 1, 6, 1, 18, 3

Offset

1,6

Comments

Lucas showed that A001602 divides p-1 or p+1, according as (5|p) = 1 or -1 respectively. This is the quotient.

Links

Patrick McKinley, Table of n, a(n) for n = 1..10000

Formula

a(n) = (prime(n) - (5|prime(n))) / A001602(n).

Example

a(6) = 2, as 13 is the 6th prime, 5 is not a quadratic residue mod 13, 13 first occurs as a prime factor of Fibonacci(7) and (13 - (-1)) / 7 = 2.

Crossrefs

Cf. A001602.

Sequence in context: A074295 A331348 A236479 * A334028 A351014 A124767

Adjacent sequences: A116511 A116512 A116513 * A116515 A116516 A116517

Keyword

easy,nonn

Author

Nick Krempel, Mar 24 2006

Extensions

a(1)=1 added by N. J. A. Sloane, Dec 07 2020

Status

approved