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

Author

José María Grau Ribas, Jan 21 2012

Keywords

• nonn

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.

Crossrefs

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

Programs

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

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[#]&]