A050426 Numbers for which in base 2 the least number of digits that can be removed to leave a base 2 palindromic number (beginning with 1) is 2.

4, 12, 20, 22, 26, 28, 36, 38, 39, 46, 50, 57, 58, 60, 68, 70, 71, 74, 75, 79, 82, 84, 86, 87, 94, 98, 105, 106, 108, 110, 113, 117, 118, 121, 122, 124, 132, 134, 135, 138, 139, 141, 154, 155, 159, 162, 166, 167, 175, 177, 178, 179, 180, 182, 190, 194, 202

Offset

1,1

Links

Table of n, a(n) for n=1..57.

Example

(70 base 2) = 1000110 -> 10001.

Prog

(Python)
from itertools import combinations
def ok(n):
    b = bin(n)[2:]
    for digs_to_remove in range(4):
        for skip in combinations(range(len(b)), digs_to_remove):
            newb = "".join(b[i] for i in range(len(b)) if i not in skip)
            if len(newb) > 0 and newb[0] == '1' and newb == newb[::-1]:
                return (digs_to_remove == 2)
    return False
print(list(filter(ok, range(203)))) # Michael S. Branicky, Aug 24 2021

Crossrefs

Cf. A050421, A050425, A050427, A050428, A050429.

Sequence in context: A133096 A309085 A104814 * A061820 A273541 A273215

Adjacent sequences: A050423 A050424 A050425 * A050427 A050428 A050429

Keyword

nonn,base

Author

Clark Kimberling

Status

approved