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

0, 3, 5, 6, 9, 30, 33, 36, 39, 53, 60, 63, 65, 66, 90, 95, 96, 99, 105, 120, 172, 175, 177, 178, 180, 209, 240, 243, 277, 300, 303, 306, 330, 340, 343, 360, 363, 366, 390, 396, 399, 430, 480, 483, 485, 486, 533, 534, 543, 571, 600, 603, 605, 606, 630, 633, 636, 658, 660, 663

Offset: 1

Author

Vladimir Shevelev, Oct 10 2014

Keywords

• nonn
• base

Comments

Dual variant of A248642.

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.

Examples

			172 is in the sequence since 172,72,12,17 are evil.
		

Crossrefs

Cf. A001969, A248478, A248642, A248659.

Programs

Sage

def is_evil(n):
    if n==0:
        return True
    else:
        return sum(Integer(n).digits(base=2))%2==0
def remain_evil(n):
    if not(is_evil(n)):
        return False
    else:
        L=Integer(n).digits(base=10)
        M=[]
        for i in [0..len(L)-1]:
            G=L[0:i]+L[i+1:]
            M.append(is_evil(sum(G[i]*10^i for i in [0..len(G)-1])))
        return sum(M)==len(M)
[x for x in [0..500] if remain_evil(x)] # Tom Edgar, Oct 10 2014

Extensions

More terms from Peter J. C. Moses, Oct 10 2014