A364086 Fixed points of A002326, i.e., numbers k such that A002326(k) = k.

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

Author

Daniel Haase, Jul 09 2023

Keywords

• nonn
• easy

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.

Examples

			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.
		

Links

• Daniel Haase, Table of n, a(n) for n = 1..10000

Crossrefs

Cf. A002326, A115591, A001122.

Programs

Mathematica

Select[Range[600], MultiplicativeOrder[2, 2*# + 1] == # &] (* Amiram Eldar, Jul 28 2023 *)

PARI

isok(k) = znorder(Mod(2, 2*k+1)) == k; \\ Michel Marcus, Jul 28 2023