A050420 Numbers for which in base 2 the least number of digits that can be removed to leave a palindrome (possibly beginning with 0) is 1.

2, 4, 6, 8, 10, 11, 13, 14, 16, 18, 19, 22, 23, 25, 29, 30, 32, 34, 35, 36, 37, 41, 42, 43, 46, 47, 49, 53, 54, 55, 59, 61, 62, 64, 66, 67, 69, 76, 77, 81, 82, 83, 89, 90, 91, 94, 95, 97, 101, 102, 103, 109, 111, 115, 123, 125, 126, 128, 130, 131, 133, 136

Offset

1,1

Links

Robert Israel, Table of n, a(n) for n = 1..10000

Example

(18 base 2) = 10010 -> 1001.

Maple

filter:= proc(n) local L, R, k, m;
  L:= convert(n, base, 2);
  R:= ListTools:-Reverse(L);
  m:= nops(L);
  if L = R then return false fi;
  ormap(i -> subsop(i=NULL, L)=subsop(m+1-i=NULL, R), [$1..m]);
end proc:
select(filter, [$1..200]); # Robert Israel, Oct 28 2020

Prog

(Python)
def ok(n):
    b = bin(n)[2:]
    if b == b[::-1]: return False
    for skip in range(len(b)):
        newb = b[:skip] + b[skip+1:]
        if len(newb) > 0 and newb == newb[::-1]:
            return True
    return False
print(list(filter(ok, range(137)))) # Michael S. Branicky, Aug 24 2021

Crossrefs

Includes A164302.

Supersequence of A050425 (beginning with 1).

Cf. A050421, A050422, A050423, A050424.

Sequence in context: A067030 A072427 A337430 * A214671 A291171 A334614

Adjacent sequences: A050417 A050418 A050419 * A050421 A050422 A050423

Keyword

nonn,base

Author

Clark Kimberling

Status

approved