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A250292
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Numbers k such that Pell(k) is a semiprime.
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1
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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
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OFFSET
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1,1
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COMMENTS
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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
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LINKS
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EXAMPLE
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17 is a term since Pell(17) = 1136689 = 137 * 8297 is a semiprime.
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MAPLE
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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:
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MATHEMATICA
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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 *)
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CROSSREFS
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KEYWORD
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nonn,more,hard
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AUTHOR
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EXTENSIONS
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STATUS
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approved
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