A185359 Numbers k such that {m^m mod k: m >= 1} is not purely periodic.

8, 16, 24, 32, 40, 48, 56, 64, 72, 80, 81, 88, 96, 104, 112, 120, 128, 136, 144, 152, 160, 162, 168, 176, 184, 192, 200, 208, 216, 224, 232, 240, 243, 248, 256, 264, 272, 280, 288, 296, 304, 312, 320, 324, 328, 336, 344, 352, 360, 368, 376, 384, 392, 400

Offset

1,1

Comments

k is a term if and only if k = Product_{i=1..t} p_i^e_i with e_i > p_i for some i.

A182938(a(n)) = 0. - Reinhard Zumkeller, Feb 18 2012

The asymptotic density of this sequence is 1 - Product_{p prime} 1 - 1/p^(p+1) = 0.13585792767780221591... - Amiram Eldar, Nov 24 2020

Links

Reinhard Zumkeller, Table of n, a(n) for n = 1..10000

R. Hampel, The length of the shortest period of rests of numbers n^n, Ann. Polon. Math. 1 (1955), 360-366.

Mathematica

j[p_, e_]:=e>p; j[n_]:={False}==Union@Module[{fa=FactorInteger[n]}, Table[j[fa[[i, 1]], fa[[i, 2]]], {i, 1, Length[fa]}]]; Select[Range[1000], !j[#]&]

Prog

(Haskell)
a185359 n = a185359_list !! (n-1)
a185359_list = [x | x <- [1..], or $ zipWith (<)
                    (a027748_row x) (map toInteger $ a124010_row x)]
-- Reinhard Zumkeller, Feb 18 2012

Crossrefs

Cf. A027748, A124010, A008590 (subsequence), A185358, A207481 (complement).

Sequence in context: A282148 A277780 A044893 * A365886 A022144 A181390

Adjacent sequences: A185356 A185357 A185358 * A185360 A185361 A185362

Keyword

nonn

Author

José María Grau Ribas, Jan 21 2012

Status

approved