A072496 - OEIS

%I #20 Mar 06 2020 09:26:49

%S 0,1,4,5,6,9,11,16,19,21,24,25,29,31,36,39,41,44,49,51,56,59,61,64,69,

%T 71,75,76,79,81,84,89,91,96,99,101,125,149,151,176,199,201,224,249,

%U 251,299,301,349,351,375,376,399,401,424,449,451,499,501,549,551

%N k-morphic numbers for any k such that (k-1)/10 is an odd integer not divisible by 5.

%C Definition: n is a k-morphic number if n^k ends with n.

%o (PARI) k=11; for(n=1,10000,if((n^k)%(10^ceil(log(n)/log(10)))==n, print1(n,","))); \\ starting with 4, 5, ...

%o (Sage)

%o def automorphic(maxdigits, pow, base=10) :

%o     morphs = [[0]]

%o     for i in range(maxdigits):

%o         T=[d*base^i+x for x in morphs[-1] for d in range(base)]

%o         morphs.append([x for x in T if x^pow % base^(i+1) == x])

%o     res = list(set(sum(morphs, []))); res.sort()

%o     return res

%o # (call with pow=11 for this sequence), _Eric M. Schmidt_, Jul 30 2013

%Y Cf. A072495.

%Y 3-morphic numbers = 7-morphic numbers, see A033819; 5-morphic numbers = 13-morphic numbers, see A068407.

%K nonn

%O 1,3

%A _Benoit Cloitre_, Oct 19 2002

%E Sequence corrected by _Eric M. Schmidt_, Jul 30 2013