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A262708 a(n) = p-(p/5) where p = prime(n) and (p/5) is a Legendre symbol. 1
8, 10, 14, 18, 18, 24, 28, 30, 38, 40, 44, 48, 54, 58, 60, 68, 70, 74, 78, 84, 88, 98, 100, 104, 108, 108, 114, 128, 130, 138, 138, 148, 150, 158, 164, 168, 174, 178, 180, 190, 194, 198, 198, 210, 224, 228, 228, 234, 238, 240, 250, 258, 264, 268, 270, 278, 280 (list; graph; refs; listen; history; text; internal format)
OFFSET
4,1
COMMENTS
The sequence lists Fibonacci indices q that are conjectured to produce Fibonacci numbers divisible by p^2, where p is a Fibonacci-Wieferich prime.
REFERENCES
Paulo Ribenboim, My Numbers, My Friends, Springer-Verlag, 2000.
Steven Vajda, Fibonacci and Lucas Numbers, and the Golden Section: Theory and Applications, Dover. (See p. 73.)
LINKS
U. Alfred, On the form of primitive factors of Fibonacci numbers, Volume 1, Fibonacci Quarterly, vol 1 (1963), page 1.
Andreas-Stephan Elsenhans, The Fibonacci sequence modulo p^2., pages 1-6.
Richard J. McIntosh and Eric L. Roettger, A search for Fibonacci-Wieferich and Wolstenholme primes, Mathematics of Computation, vol 76 (260), Oct 2007.
John Vinson, The Relation of the Period Modulo m to the Rank of Apparition of m in the Fibonacci Sequence, Fibonacci Quarterly, vol 1 (1963), pages 37-45.
EXAMPLE
For n=4, prime(4)=7, and a(4)=8.
MATHEMATICA
Table[Prime@ n - JacobiSymbol[Prime@ n, 5], {n, 4, 60}] (* Michael De Vlieger, Oct 04 2015 *)
PROG
(PARI) lista(nn)=forprime(p=3, nn, print1(p-kronecker(p, 5), ", "); ); \\ Michel Marcus, Sep 29 2015
CROSSREFS
Sequence in context: A087695 A322998 A368280 * A134321 A326386 A027693
KEYWORD
nonn
AUTHOR
Shane Findley, Sep 27 2015
EXTENSIONS
Edited by N. J. A. Sloane, Sep 29 2015
Edited by Jon E. Schoenfield, Oct 09 2015
STATUS
approved

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Last modified March 28 10:55 EDT 2024. Contains 371241 sequences. (Running on oeis4.)