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A298758
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Numbers k such that both k and 2k-1 are Poulet numbers (Fermat pseudoprimes to base 2).
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5
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15709, 65281, 20770621, 104484601, 112037185, 196049701, 425967301, 2593182901, 16923897871, 32548281361, 45812984491, 52035130951, 55897227751, 82907336737, 90003640021, 92010062101, 138016057141, 204082130071, 310026150211, 620006892121, 622333751509
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OFFSET
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1,1
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COMMENTS
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Numbers k such that both k and 2k+1 are Poulet numbers are listed in A303447.
If p is a prime such that 2*p-1 is also a prime (A005382) and k = (2^(2*p-1)+1)/3 and 2*k-1 are both composites, then k is a term of this sequence (Rotkiewicz, 2000). - Amiram Eldar, Nov 09 2023
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LINKS
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MATHEMATICA
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s = Import["b001567.txt", "Data"][[All, -1]]; n = Length[s];
aQ[n_] := ! PrimeQ[n] && PowerMod[2, (n - 1), n] == 1;
a = {}; Do[p = 2*s[[k]] - 1; If[aQ[p], AppendTo[a, s[[k]]]], {k, 1, n}]; a (* using the b-File from A001567 *)
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PROG
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(PARI) isP(n) = (Mod(2, n)^n==2) && !isprime(n) && (n>1);
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CROSSREFS
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KEYWORD
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nonn
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AUTHOR
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STATUS
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approved
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