A050423 Numbers for which in base 2 the least number of digits that can be removed to leave a palindrome (possibly beginning with 0) is 4.

232, 240, 368, 424, 432, 440, 452, 456, 464, 468, 472, 480, 482, 484, 488, 496, 542, 543, 558, 559, 688, 720, 736, 752, 816, 848, 864, 868, 872, 888, 900, 912, 920, 928, 932, 960, 962, 970, 972, 977, 978, 980, 984, 993, 994, 996, 1000, 1008, 1052, 1054, 1055, 1068, 1070, 1071, 1078, 1079

Offset

1,1

Links

Table of n, a(n) for n=1..56.

Example

464 is a term because 464 = 111010000_2 and deleting the four 1's gives the palindrome 00000 and there is no way to delete fewer bits and get a palindrome. - Sean A. Irvine, Aug 15 2021

Prog

(Python)
from itertools import combinations
def ok(n):
    b = bin(n)[2:]
    for digs_to_remove in range(5):
        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 newb == newb[::-1]: return (digs_to_remove == 4)
    return False
print(list(filter(ok, range(1080)))) # Michael S. Branicky, Aug 15 2021

Crossrefs

Sequence in context: A172935 A319306 A280538 * A126818 A277076 A250645

Adjacent sequences: A050420 A050421 A050422 * A050424 A050425 A050426

Keyword

nonn,base

Author

Clark Kimberling

Extensions

Missing terms inserted by Sean A. Irvine, Aug 15 2021

Status

approved