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A191834 Numbers n not divisible by 2 or 3 such that k^k == k+1 (mod n) has no nonzero solutions. 3

%I

%S 205,301,455,1015,1025,1085,1435,1505,2107,2255,2275,2485,2665,3185,

%T 3311,3485,3895,3913,4715,4823,5005,5075,5117,5125,5425,5467,5719,

%U 5915,5945,6355,6923,7105,7175,7525,7585,7595,7735,8405,8645,8729,8815,9331,9635,10045,10465,10535,10865,11137,11165,11275,11375,11935,12095

%N Numbers n not divisible by 2 or 3 such that k^k == k+1 (mod n) has no nonzero solutions.

%C Values of A007310(n) for n such that A191833(n) = 0.

%C This sequence contains no primes. If p is a prime, and r is a primitive root of p, the numbers (r+j*p)^(r+j*p) for j = 1..p-1 include all residues of units mod p, and for p > 3, r+1 must be a unit.

%C The complete list of n such that k^k == k+1 (mod n) has no nonzero solutions is the union of A047229 and this sequence.

%H Jean-Fran├žois Alcover, <a href="/A191834/b191834.txt">Table of n, a(n) for n = 1..150</a>

%t A191833[n_] := (For[m = 2*n + 2*Floor[n/2] - 1; k = 1, k <= m^2, k++, If[PowerMod[k, k, m] == Mod[k+1, m], Return[{k, m}]]]; {0, m}); Reap[For[j = 1; n = 1, n <= 5000, n++, {z, m} = A191833[n]; If[z == 0, Print["a(", j++, ") = ", m]; Sow[m]]]][[2, 1]] (* _Jean-Fran├žois Alcover_, Sep 13 2013 *)

%Y Cf. A191833, A191835 (primitive elements).

%K nonn

%O 1,1

%A _Franklin T. Adams-Watters_, Jun 17 2011

%E Terms a(30) onward from _Max Alekseyev_, Sep 10 2013

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Last modified June 4 17:50 EDT 2020. Contains 334828 sequences. (Running on oeis4.)