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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
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 (list; graph; refs; listen; history; text; internal format)
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

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Last modified March 28 07:59 EDT 2020. Contains 333079 sequences. (Running on oeis4.)