login
The OEIS is supported by the many generous donors to the OEIS Foundation.

 

Logo
Hints
(Greetings from The On-Line Encyclopedia of Integer Sequences!)
A250292 Numbers k such that Pell(k) is a semiprime. 1
7, 9, 17, 19, 23, 43, 47, 67, 73, 83, 103, 109, 139, 149, 157, 173, 179, 223, 239, 281, 311, 313, 349, 431, 557, 569, 577, 587 (list; graph; refs; listen; history; text; internal format)
OFFSET
1,1
COMMENTS
a(29) >= 709. - Hugo Pfoertner, Jul 29 2019
859, 937, 1087, 1151, and 1193 belong to the sequence. 709 and 787 have not yet been ruled out. The next candidate after these appears to be 1471. - Daniel M. Jensen, Oct 18 2019
LINKS
EXAMPLE
17 is a term since Pell(17) = 1136689 = 137 * 8297 is a semiprime.
MAPLE
pell:= gfun:-rectoproc({a(0)=0, a(1)=1, a(n)=2*a(n-1)+a(n-2)}, a(n), remember):
filter:= proc(n) local F, f;
F:= ifactors(pell(n), easy)[2];
if add(f[2], f=F) > 2 then return false fi;
if hastype(F, symbol) then
if add(f[2], f=F) >= 2 then return false fi;
else return evalb(add(f[2], f=F)=2)
fi;
F:= ifactors(pell(n))[2];
evalb(add(f[2], f=F)=2)
end proc:
select(filter, [$1..230]); # Robert Israel, Jan 18 2016
MATHEMATICA
a[0] = 0; a[1] = 1; a[n_] := a[n] = 2 a[n - 1] + a[n - 2]; Select[Range[0, 160], PrimeOmega@ a@ # == 2 &] (* Michael De Vlieger, Jan 19 2016 *)
CROSSREFS
Sequence in context: A366674 A145830 A195563 * A140364 A366526 A022321
KEYWORD
nonn,more,hard
AUTHOR
Eric Chen, Dec 24 2014
EXTENSIONS
a(22)-a(23) from Daniel M. Jensen, Jan 18 2016
a(24) from Arkadiusz Wesolowski, Jan 19 2016
a(25)-a(27) from Sean A. Irvine, Jul 17 2017
a(28) from Sean A. Irvine, Jan 24 2018
STATUS
approved

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

License Agreements, Terms of Use, Privacy Policy. .

Last modified March 18 22:34 EDT 2024. Contains 370951 sequences. (Running on oeis4.)