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A096650 Indices of prime Pell numbers. 10
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 Twenty-fourth Annual International Conference on Technology in Collegiate Mathematics, Orlando, Florida, March 22-25, 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(n-1) + a(n-2)}, 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: A178317 A032024 A131741 * 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

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Last modified July 26 11:39 EDT 2016. Contains 275043 sequences.