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A354480
a(n) is the smallest decimal palindrome with Hamming weight n (i.e., with exactly n 1's when written in binary).
0
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
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
KEYWORD
nonn,base
AUTHOR
Ilya Gutkovskiy, Jun 02 2022
EXTENSIONS
a(21)-a(32) from Michael S. Branicky, Jun 02 2022
STATUS
approved