login
A261581
Primes such that z(p) is not divisible by 4 where z(n) is A214028(n), the smallest k such that n divides A000129(k), the k-th Pell number.
1
2, 5, 7, 13, 23, 29, 31, 37, 41, 47, 53, 61, 71, 79, 101, 103, 109, 127, 137, 149, 151, 157, 167, 173, 181, 191, 197, 199, 223, 229, 239, 263, 269, 271, 277, 293, 311, 313, 317, 349, 353, 359, 367, 373, 383, 389, 397, 409, 421, 431, 439, 457, 461, 463, 479, 487
OFFSET
1,1
LINKS
Bernadette Faye and Florian Luca, Pell Numbers whose Euler Function is a Pell Number, arXiv:1508.05714 [math.NT], 2015.
EXAMPLE
The smallest Pell number divisible by the prime 2 has index 2, which is not divisible by 4, so 2 is in the sequence.
PROG
(PARI) pell(n) = polcoeff(Vec(x/(1-2*x-x^2) + O(x^(n+1))), n);
z(n) = {k=1; while (pell(k) % n, k++); k; }
lista(nn) = {forprime(p=2, nn, if (z(p) % 4, print1(p, ", ")); ); }
CROSSREFS
KEYWORD
nonn
AUTHOR
Michel Marcus, Aug 25 2015
STATUS
approved