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A364086
Fixed points of A002326, i.e., numbers k such that A002326(k) = k.
1
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
OFFSET
1,1
COMMENTS
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.
LINKS
EXAMPLE
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.
MATHEMATICA
Select[Range[600], MultiplicativeOrder[2, 2*# + 1] == # &] (* Amiram Eldar, Jul 28 2023 *)
PROG
(PARI) isok(k) = znorder(Mod(2, 2*k+1)) == k; \\ Michel Marcus, Jul 28 2023
CROSSREFS
KEYWORD
nonn,easy
AUTHOR
Daniel Haase, Jul 09 2023
STATUS
approved