A373205 - OEIS

%I #28 Jun 04 2024 07:40:03

%S 1,51,57,101,151,176,201,301,351,401,501,551,576,601,625,701,751,801,

%T 901,951,976,1001,1376,2001,2057,2751,3001,4001,4193,4751,5001,5376,

%U 6001,6249,6751,7001,8001,8751,9001,9375,9376,10001,10751,11001,12001,13001

%N Numbers m such that m^m == m (mod 10^(len(m) + 1)), where len(m) is the number of digits of m (A055642).

%C By definition, the present sequence is a subsequence of A082576.

%C For each integer r >= 2 this sequence contains 10^r + 1.

%C All terms > 1 end in 01, 25, 49, 51, 57, 75, 76, or 93.

%H <a href="/index/Ar#automorphic">Index entries for sequences related to automorphic numbers</a>

%e 51 is a term since 51 is a 2-digit number and 51^51 == 5051 (mod 10^4) and thus 51^51 == 51 (mod 10^(2 + 1)).

%o (PARI) for (len_m = 1, 5, for (m = 10^(len_m - 1), 10^len_m - 1, if (m == Mod(m, 10^(len_m + 1))^m, print1(m, ", "))))

%o (Python)

%o from itertools import count

%o def A373205_gen(): # generator of terms

%o     for i in count(0,100):

%o         for j in (1, 25, 49, 51, 57, 75, 76, 93):

%o             m = i+j

%o             if pow(m,m,10*10**(len(str(m)))) == m:

%o                 yield m

%o A373205_list = list(islice(A373205_gen(),20)) # _Chai Wah Wu_, Jun 02 2024

%Y Cf. A055642, A082576, A373206.

%K nonn,base

%O 1,2

%A _Marco Ripà_, May 27 2024