login
The OEIS Foundation is supported by donations from users of the OEIS and by a grant from the Simons Foundation.

 

Logo

Thanks to everyone who made a donation during our annual appeal!
To see the list of donors, or make a donation, see the OEIS Foundation home page.

Hints
(Greetings from The On-Line Encyclopedia of Integer Sequences!)
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

%I

%S 2,5,7,13,23,29,31,37,41,47,53,61,71,79,101,103,109,127,137,149,151,

%T 157,167,173,181,191,197,199,223,229,239,263,269,271,277,293,311,313,

%U 317,349,353,359,367,373,383,389,397,409,421,431,439,457,461,463,479,487

%N 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 Bernadette Faye, 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 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 (PARI) pell(n) = polcoeff(Vec(x/(1-2*x-x^2) + O(x^(n+1))), n);

%o z(n) = {k=1; while (pell(k) % n, k++); k;}

%o lista(nn) = {forprime(p=2, nn, if (z(p) % 4, print1(p, ", ")););}

%Y Cf. A000129, A214028, A261580.

%K nonn

%O 1,1

%A _Michel Marcus_, Aug 25 2015

Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Style Sheet | Transforms | Superseeker | Recent
The OEIS Community | Maintained by The OEIS Foundation Inc.

License Agreements, Terms of Use, Privacy Policy. .

Last modified January 20 11:11 EST 2020. Contains 331083 sequences. (Running on oeis4.)