A354480 a(n) is the smallest decimal palindrome with Hamming weight n (i.e., with exactly n 1's when written in binary).

0, 1, 3, 7, 77, 55, 111, 191, 383, 767, 5115, 11711, 15351, 30703, 81918, 97279, 744447, 978879, 1570751, 3665663, 8387838, 66911966, 66322366, 132111231, 199212991, 389545983, 939474939, 3204444023, 3220660223, 11542724511, 34258485243, 33788788733, 34292629243

Offset

0,3

Links

Table of n, a(n) for n=0..32.

Index entries for sequences related to binary expansion of n

Index entries for sequences related to palindromes

Prog

(Python)
from itertools import count, islice, product
def pals(startd=1): # generator for base-10 palindromes
    for d in count(startd):
        for p in product("0123456789", repeat=d//2):
            if d//2 > 0 and p[0] == "0": continue
            left = "".join(p); right = left[::-1]
            for mid in [[""], "0123456789"][d%2]:
                yield int(left + mid + right)
def a(n):
    for p in pals(startd=len(str(2**n-1))):
        if bin(p).count("1") == n:
            return p
print([a(n) for n in range(33)]) # Michael S. Branicky, Jun 02 2022

Crossrefs

Cf. A000120, A000225, A002113, A061712, A062388, A089226, A089998, A089999, A102029, A114477.

Sequence in context: A325476 A234536 A103737 * A108537 A364660 A219292

Adjacent sequences: A354477 A354478 A354479 * A354481 A354482 A354483

Keyword

nonn,base

Author

Ilya Gutkovskiy, Jun 02 2022

Extensions

a(21)-a(32) from Michael S. Branicky, Jun 02 2022

Status

approved