A071774 Related to Pisano periods: integers k such that the period of Fibonacci numbers mod k equals 2*(k+1).
3, 7, 13, 17, 23, 37, 43, 53, 67, 73, 83, 97, 103, 127, 137, 157, 163, 167, 173, 193, 197, 223, 227, 257, 277, 283, 293, 313, 317, 337, 367, 373, 383, 397, 433, 443, 457, 463, 467, 487, 503, 523, 547, 577, 587, 593, 607, 613, 617, 643, 647, 653, 673, 683, 727
Offset: 1
Links
- Michael De Vlieger, Table of n, a(n) for n = 1..3969
- Bob Bastasz, Lyndon words of a second-order recurrence, Fibonacci Quarterly (2020) Vol. 58, No. 5, 25-29.
Programs
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Mathematica
Select[Prime@ Range[129], Function[n, Mod[Last@ NestWhile[{Mod[#2, n], Mod[#1 + #2, n], #3 + 1} & @@ # &, {1, 1, 1}, #[[1 ;; 2]] != {0, 1} &], n] == Mod[2 (n + 1), n] ]] (* Michael De Vlieger, Mar 31 2021, after Leo C. Stein at A001175 *) -
PARI
for(n=2,5000,t=2*(n+1);good=1;if(fibonacci(t)%n==0, for(s=0,t,if(fibonacci(t+s)%n!=fibonacci(s)%n,good=0;break); if(s>1&&s
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PARI
forprime(p=3,3000,if(p%5==2||p%5==3,a=1;b=0;c=1;while(a!=0||b!=1,c++;d=a;a=b;a=(a+d)%p;b=d%p);if(c==(2*(p+1)),print1(p",")))) /* V. Raman, Nov 22 2012 */
Extensions
More terms from Lambert Klasen (Lambert.Klasen(AT)gmx.net), Dec 21 2004
Comments