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

1,2

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.

Links

Table of n, a(n) for n=1..60.

Example

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

Prog

(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

Crossrefs

Cf. A001969, A248478, A248642, A248659.

Sequence in context: A102372 A095829 A054871 * A242197 A283051 A376377

Adjacent sequences: A248641 A248642 A248643 * A248645 A248646 A248647

Keyword

nonn,base

Author

Vladimir Shevelev, Oct 10 2014

Extensions

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

Status

approved