cp's OEIS Frontend

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.

%I A261581 #12 Jun 16 2024 06:34:39
%S A261581 2,5,7,13,23,29,31,37,41,47,53,61,71,79,101,103,109,127,137,149,151,
%T A261581 157,167,173,181,191,197,199,223,229,239,263,269,271,277,293,311,313,
%U A261581 317,349,353,359,367,373,383,389,397,409,421,431,439,457,461,463,479,487
%N 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.
%H A261581 Bernadette Faye and Florian Luca, <a href="http://arxiv.org/abs/1508.05714">Pell Numbers whose Euler Function is a Pell Number</a>, arXiv:1508.05714 [math.NT], 2015.
%e A261581 The smallest Pell number divisible by the prime 2 has index 2, which is not divisible by 4, so 2 is in the sequence.
%o A261581 (PARI) pell(n) = polcoeff(Vec(x/(1-2*x-x^2) + O(x^(n+1))), n);
%o A261581 z(n) = {k=1; while (pell(k) % n, k++); k;}
%o A261581 lista(nn) = {forprime(p=2, nn, if (z(p) % 4, print1(p, ", ")););}
%Y A261581 Cf. A000129, A214028, A261580.
%K A261581 nonn
%O A261581 1,1
%A A261581 _Michel Marcus_, Aug 25 2015