A262708 - OEIS

A262708

a(n) = p-(p/5) where p = prime(n) and (p/5) is a Legendre symbol.

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

Table of n, a(n) for n=4..60.

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.

Shane Findley, Discussion of Sequence A262708.

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

Cf. A001602, A051694.

Sequence in context: A087695 A322998 A368280 * A134321 A326386 A027693

Adjacent sequences: A262705 A262706 A262707 * A262709 A262710 A262711

KEYWORD