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

205, 301, 455, 1015, 1025, 1085, 1435, 1505, 2107, 2255, 2275, 2485, 2665, 3185, 3311, 3485, 3895, 3913, 4715, 4823, 5005, 5075, 5117, 5125, 5425, 5467, 5719, 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

Offset

1,1

Comments

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

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.

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.

Links

Jean-François Alcover, Table of n, a(n) for n = 1..150

Mathematica

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-François Alcover, Sep 13 2013 *)

Crossrefs

Cf. A191833, A191835 (primitive elements).

Sequence in context: A072573 A249052 A116177 * A042983 A186475 A020170

Adjacent sequences: A191831 A191832 A191833 * A191835 A191836 A191837

Keyword

nonn

Author

Franklin T. Adams-Watters, Jun 17 2011

Extensions

Terms a(30) onward from Max Alekseyev, Sep 10 2013

Status

approved