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 A250292 Numbers k such that Pell(k) is a semiprime. 0
 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 FactorDB, Status of Pell(709). FactorDB, Status of Pell(787). 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 Cf. A001358, A096650, A072381, A085726, A000129. Sequence in context: A020691 A145830 A195563 * A140364 A022321 A194830 Adjacent sequences:  A250289 A250290 A250291 * A250293 A250294 A250295 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

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Last modified August 7 23:50 EDT 2022. Contains 355995 sequences. (Running on oeis4.)