close
login
A185359
Numbers k such that {m^m mod k: m >= 1} is not purely periodic.
10
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
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: A044893 A382417 A387326 * A365886 A181390 A008590
KEYWORD
nonn
AUTHOR
STATUS
approved