|
| |
|
|
A096650
|
|
Indices of prime Pell numbers.
|
|
14
|
|
|
|
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: 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
|
| |
|
|
