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A179707
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Semiprimes p*q such that 2^p mod q == 2^q mod p.
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3
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4, 9, 25, 49, 121, 169, 289, 341, 361, 529, 731, 841, 961, 1333, 1369, 1387, 1681, 1727, 1849, 2047, 2209, 2701, 2809, 3277, 3481, 3503, 3721, 3763, 4033, 4369, 4489, 4681, 5041, 5329, 5461, 6241, 6889, 7921, 7957, 8321, 9409, 9509, 10201, 10261, 10609, 10669, 11449, 11881
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OFFSET
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1,1
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COMMENTS
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The square of every prime is here, as are the semiprimes in A179839.
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LINKS
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EXAMPLE
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341 is a term because 341 = 11*31 and 2^11 mod 31 = 2^31 mod 11.
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MATHEMATICA
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fQ[n_] := Block[{fi = Flatten[ Table[ First@ #, {Last@ #}] & /@ FactorInteger@ n]}, Length@ fi == 2 && PowerMod[2, fi[[2]], fi[[1]]] == PowerMod[2, fi[[1]], fi[[2]]]]; Select[ Range@ 12000, fQ]
With[{nn=50}, Take[Union[Times@@@Select[Tuples[Prime[Range[2nn]], 2], PowerMod[ 2, #[[1]], #[[2]]]==PowerMod[2, #[[2]], #[[1]]]&]], nn]] (* Harvey P. Dale, Sep 03 2015 *)
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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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