

A096650


Indices of prime Pell numbers.


11



2, 3, 5, 11, 13, 29, 41, 53, 59, 89, 97, 101, 167, 181, 191, 523, 929, 1217, 1301, 1361, 2087, 2273, 2393, 8093, 13339, 14033, 23747, 28183, 34429, 36749, 90197
(list;
graph;
refs;
listen;
history;
text;
internal format)



OFFSET

1,1


COMMENTS

For a Pell number to be prime, the index must be prime. The indices greater than 523 yield probable primes. No others less than 100000.  T. D. Noe, Sep 13 2004
n divides m if and only if A000129(n) divides A000129(m). This is the reason of the fact that this sequence is a subsequence of A000040. For complement of this sequence see A270387.  Altug Alkan, Apr 29 2016


LINKS

Table of n, a(n) for n=1..31.
J. L. Schiffman, Exploring the Fibonacci sequence of order two with CAS technology, Paper C027, Electronic Proceedings of the Twentyfourth Annual International Conference on Technology in Collegiate Mathematics, Orlando, Florida, March 2225, 2012. See p. 262.  N. J. A. Sloane, Mar 27 2014
Eric Weisstein's World of Mathematics, Pell Number
Eric Weisstein's World of Mathematics, Integer Sequence Primes


EXAMPLE

P(11)=5741, which is prime.


MAPLE

Pell:= gfun:rectoproc( {a(0) = 0, a(1) = 1, a(n) = 2*a(n1) + a(n2)}, a(n), remember):
select(t > isprime(t) and isprime(Pell(t)), [2, seq(2*i+1, i=1..2000)]); # Robert Israel, Aug 28 2015


MATHEMATICA

lst={}; a=0; b=1; Do[c=a+2b; a=b; b=c; If[PrimeQ[c], AppendTo[lst, n]], {n, 2, 10000}]; lst (* T. D. Noe, Aug 17 2004 *)
Flatten@ Position[#, p_ /; PrimeQ@ p]  1 &@ CoefficientList[Series[x/(1  2 x  x^2), {x, 0, 5000}], x] (* Michael De Vlieger, Apr 29 2016, after Stefan Steinerberger at A000129 *)


CROSSREFS

Cf. A000129 (Pell numbers), A086383 (prime Pell numbers), A270387.
Sequence in context: A032024 A131741 A277098 * A111107 A186641 A215354
Adjacent sequences: A096647 A096648 A096649 * A096651 A096652 A096653


KEYWORD

nonn


AUTHOR

Julien Peter Benney (jpbenney(AT)ftml.net), Aug 15 2004


EXTENSIONS

More terms from T. D. Noe, Aug 17 2004
Further terms from T. D. Noe, Sep 13 2004


STATUS

approved



