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A248644 Evil numbers (A001969) remaining evil if any digit is deleted (zeros allowed).

%I A248644 #21 Mar 14 2020 15:52:52
%S A248644 0,3,5,6,9,30,33,36,39,53,60,63,65,66,90,95,96,99,105,120,172,175,177,
%T A248644 178,180,209,240,243,277,300,303,306,330,340,343,360,363,366,390,396,
%U A248644 399,430,480,483,485,486,533,534,543,571,600,603,605,606,630,633,636,658,660,663
%N A248644 Evil numbers (A001969) remaining evil if any digit is deleted (zeros allowed).
%C A248644 Dual variant of A248642.
%C A248644 Although for numbers >9 we never put 0 instead of the removed digit, we include single-digit numbers 0,3,5,6,9 since, e.g., 3=03, etc.
%e A248644 172 is in the sequence since 172,72,12,17 are evil.
%o A248644 (Sage)
%o A248644 def is_evil(n):
%o A248644     if n==0:
%o A248644         return True
%o A248644     else:
%o A248644         return sum(Integer(n).digits(base=2))%2==0
%o A248644 def remain_evil(n):
%o A248644     if not(is_evil(n)):
%o A248644         return False
%o A248644     else:
%o A248644         L=Integer(n).digits(base=10)
%o A248644         M=[]
%o A248644         for i in [0..len(L)-1]:
%o A248644             G=L[0:i]+L[i+1:]
%o A248644             M.append(is_evil(sum(G[i]*10^i for i in [0..len(G)-1])))
%o A248644         return sum(M)==len(M)
%o A248644 [x for x in [0..500] if remain_evil(x)] # _Tom Edgar_, Oct 10 2014
%Y A248644 Cf. A001969, A248478, A248642, A248659.
%K A248644 nonn,base
%O A248644 1,2
%A A248644 _Vladimir Shevelev_, Oct 10 2014
%E A248644 More terms from _Peter J. C. Moses_, Oct 10 2014