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A222361 Fibonacci-Legendre quotients: (Fibonacci(p) - L(p/5)) / p, where p = prime(n) and L(p/5) is the Legendre symbol. 3
1, 1, 1, 2, 8, 18, 94, 220, 1246, 17732, 43428, 652914, 4038540, 10081266, 63217342, 1005967758, 16215627560, 41061160360, 670829406162, 4338894664368, 11048157986978, 183194101578180, 1195118711985006, 19999768719154092, 862073644225241474, 5674731128849674100, 14568160545698020226, 96118885585174929102, 247025215671874138312, 1633201998168434481118 (list; graph; refs; listen; history; text; internal format)
OFFSET
1,4
COMMENTS
Fibonacci(p) == L(p/5) mod p, where the Legendre symbol L(p/5) equals 0, +1, -1 according as p = 5, 5*k+-1, 5*k+-2 for some k.
Not to be confused with Fibonacci(p - L(p,5)) / p, which is A092330.
LINKS
FORMULA
For n>=4, a(n) = (Fibonacci(prime(n)) +/- 1)/prime(n), where '+' is chosen if prime(n)== 2 or 3 (mod 5), '-' is chosen otherwise. For n>=2, a(n) = round(Fibonacci(prime(n)/prime(n)). - Vladimir Shevelev, Mar 12 2014
EXAMPLE
Prime(4) = 7, so a(4) = (Fibonacci(7)-L(7/5))/7 = (13-(-1))/7 = 14/7 = 2.
MATHEMATICA
Table[p = Prime[n]; (Fibonacci[p] - JacobiSymbol[p, 5])/p, {n, 1, 30}]
CROSSREFS
Sequence in context: A074128 A061226 A134827 * A134789 A058217 A306616
KEYWORD
nonn
AUTHOR
Jonathan Sondow, Feb 23 2013
STATUS
approved

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Last modified July 15 19:27 EDT 2024. Contains 374334 sequences. (Running on oeis4.)