The OEIS is supported by the many generous donors to the OEIS Foundation.

 Hints (Greetings from The On-Line Encyclopedia of Integer Sequences!)
 A214876 Prime numbers for which there is a primitive root g for which the iteration x -> g^x (mod p) generates all nonzero residues (mod p). 1
 3, 5, 23, 41, 59, 61, 107, 139, 149, 173, 181, 233, 239, 251, 269, 281, 311, 331, 349, 359, 389, 397, 439, 457, 461, 463, 467, 487, 509, 547, 577, 587, 647, 653, 719, 751, 769, 809, 811, 829, 877, 883, 907, 919, 941, 967, 1039, 1069, 1097, 1103, 1109, 1213 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,1 COMMENTS Recent works by Holden, Pomerance et al. have established that for every prime p>2 there is a primitive root g modulo p which has a fixed point: g^x = x (mod p). This sequence shows in fact not every prime has a primitive root which generates all nonzero residues by iterated exponentiation. This sequence may have applications to random number generation, where long periods are usually required. LINKS Alasdair McAndrew, Table of n, a(n) for n = 1..1884 M. Levin, C Pomerance, and K. Soundararajan, Fixed points for discrete logarithms, Lecture Notes in Computer Science, 2010, Volume 6197, Algorithmic Number Theory, pages 6-15. MATHEMATICA testcyclic[p_] := (g = 1; out = False; While[out == False && g < p-2, g += 1; If[ MultiplicativeOrder[g, p] == p-1, x = g; c = 1; While[x != 1, x = PowerMod[g, x, p]; c += 1]; If[c == p-1, out = True]]]; Return[out]); testcyclic[3] = True; Reap[ Do[ If[ testcyclic[p], Print[p]; Sow[p]], {p, Prime /@ Range[200]}]][[2, 1]] (* Jean-François Alcover, Sep 17 2012, translated from Sage *) PROG (Sage) def testcyclic(p): if p == 3: return True g = 1 out = False while not out and g2))); 0 \\ Charles R Greathouse IV, Jul 31 2016 CROSSREFS Sequence in context: A215132 A091157 A199336 * A280273 A036952 A065720 Adjacent sequences: A214873 A214874 A214875 * A214877 A214878 A214879 KEYWORD nonn,nice AUTHOR Alasdair McAndrew, Jul 28 2012 STATUS approved

Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Style Sheet | Transforms | Superseeker | Recents
The OEIS Community | Maintained by The OEIS Foundation Inc.

Last modified February 5 20:57 EST 2023. Contains 360087 sequences. (Running on oeis4.)