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A303531
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Numbers k such that both k and (k+1)/2 are Fermat pseudoprimes to base 2 (A001567).
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3
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31417, 130561, 41541241, 208969201, 224074369, 392099401, 851934601, 5186365801, 33847795741, 65096562721, 91625968981, 104070261901, 111794455501, 165814673473, 180007280041, 184020124201, 276032114281, 408164260141, 620052300421, 1240013784241, 1244667503017
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OFFSET
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1,1
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COMMENTS
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Numbers (k+1)/2 are listed in A298758.
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LINKS
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FORMULA
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MATHEMATICA
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Select[Cases[Import["https://oeis.org/A001567/b001567.txt", "Table"], {_, _}][[;; , 2]], !PrimeQ[(#+1)/2] && PowerMod[2, (#-1)/2, (#+1)/2] == 1 &] (* Amiram Eldar, Nov 09 2023 *)
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PROG
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(PARI) isF(n) = {Mod(2, n)^n==2 && !isprime(n) && n>1};
isok(n) = (n%2) && isF(n) && isF((n+1)/2); \\ Michel Marcus, Apr 26 2018
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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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