A262708 - OEIS

%I #109 Oct 16 2015 03:05:16

%S 8,10,14,18,18,24,28,30,38,40,44,48,54,58,60,68,70,74,78,84,88,98,100,

%T 104,108,108,114,128,130,138,138,148,150,158,164,168,174,178,180,190,

%U 194,198,198,210,224,228,228,234,238,240,250,258,264,268,270,278,280

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

%C The sequence lists Fibonacci indices q that are conjectured to produce Fibonacci numbers divisible by p^2, where p is a Fibonacci-Wieferich prime.

%D Paulo Ribenboim, My Numbers, My Friends, Springer-Verlag, 2000.

%D Steven Vajda, Fibonacci and Lucas Numbers, and the Golden Section: Theory and Applications, Dover. (See p. 73.)

%H U. Alfred, <a href="http://www.fq.math.ca/Scanned/1-1/alfred2.pdf">On the form of primitive factors of Fibonacci numbers</a>, Volume 1, Fibonacci Quarterly, vol 1 (1963), page 1.

%H Andreas-Stephan Elsenhans, <a href="http://www.uni-math.gwdg.de/tschinkel/gauss/Fibon.pdf">The Fibonacci sequence modulo p^2.</a>, pages 1-6.

%H Shane Findley, <a href="/A262708/a262708.txt">Discussion of Sequence A262708</a>.

%H Richard J. McIntosh and Eric L. Roettger, <a href="http://dx.doi.org/10.1090/S0025-5718-07-01955-2">A search for Fibonacci-Wieferich and Wolstenholme primes</a>, Mathematics of Computation, vol 76 (260), Oct 2007.

%H John Vinson, <a href="http://www.fq.math.ca/Scanned/1-2/vinson.pdf">The Relation of the Period Modulo m to the Rank of Apparition of m in the Fibonacci Sequence</a>, Fibonacci Quarterly, vol 1 (1963), pages 37-45.

%e For n=4, prime(4)=7, and a(4)=8.

%t Table[Prime@ n - JacobiSymbol[Prime@ n, 5], {n, 4, 60}] (* _Michael De Vlieger_, Oct 04 2015 *)

%o (PARI) lista(nn)=forprime(p=3, nn, print1(p-kronecker(p, 5), ", ");); \\ _Michel Marcus_, Sep 29 2015

%Y Cf. A001602, A051694.

%K nonn

%O 4,1

%A _Shane Findley_, Sep 27 2015

%E Edited by _N. J. A. Sloane_, Sep 29 2015

%E Edited by _Jon E. Schoenfield_, Oct 09 2015