A216067 Prime numbers p such that p is odd and is congruent to 2 (mod 5) or 3 (mod 5), but the period of the irreducible polynomial x^2-x-1 in GF(p^2) is not 2*(p+1).

47, 107, 113, 233, 263, 307, 347, 353, 557, 563, 677, 743, 797, 953, 967, 977, 1087, 1097, 1103, 1217, 1223, 1277, 1307, 1427, 1483, 1523, 1553, 1597, 1733, 1823, 1877, 1913, 1973, 2027, 2207, 2237, 2243, 2267, 2333, 2417, 2447, 2663, 2687, 2753, 2777

Offset: 1

Author

V. Raman, Sep 01 2012

Keywords

• nonn

Examples

			47 is in the sequence because the period of the Fibonacci / Lucas numbers (mod 47) = 32, is not 2*(47+1) = 96.
		

Links

• V. Raman, Table of n, a(n) for n = 1..10000

Crossrefs

Cf. A001175, A060305, A071776.

Cf. A071774.

Programs

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

Definition corrected by V. Raman, Nov 22 2012