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A364086
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Fixed points of A002326, i.e., numbers k such that A002326(k) = k.
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1
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3, 8, 11, 20, 23, 35, 39, 48, 51, 68, 83, 95, 96, 99, 119, 131, 135, 155, 156, 179, 183, 191, 200, 204, 224, 231, 239, 243, 251, 260, 284, 299, 303, 323, 359, 371, 375, 380, 384, 404, 411, 419, 428, 431, 443, 464, 483, 488, 491, 495, 504, 515, 519, 531, 543, 564
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OFFSET
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1,1
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COMMENTS
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It seems that a(n) = (A115591(n)-1)/2. Indeed, it follows from the definition of A115591 that if a prime p is listed in A115591, then (p-1)/2 is also listed in this sequence.
The related case of A002326(k) = 2k is true if (and conjecturally only if) 2k+1 is a prime with primitive root 2, see A001122.
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LINKS
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EXAMPLE
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The first three terms of this sequence are 3, 8, and 11. Thus, the first three fixed points of A002326 are A002326(3) = 3, A002326(8) = 8, and A002326(11) = 11.
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MATHEMATICA
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Select[Range[600], MultiplicativeOrder[2, 2*# + 1] == # &] (* Amiram Eldar, Jul 28 2023 *)
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PROG
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(PARI) isok(k) = znorder(Mod(2, 2*k+1)) == k; \\ Michel Marcus, Jul 28 2023
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CROSSREFS
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KEYWORD
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nonn,easy
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AUTHOR
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STATUS
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approved
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