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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 (list; graph; refs; listen; history; text; internal format)
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 A219292 A181554

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

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Last modified January 27 10:42 EST 2023. Contains 359838 sequences. (Running on oeis4.)