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A185359
Numbers k such that {m^m mod k: m >= 1} is not purely periodic.
7
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: A282148 A277780 A044893 * A365886 A022144 A181390
KEYWORD
nonn
AUTHOR
STATUS
approved