A175241 Call any positive integer that is a palindrome when written in binary a "binary palindrome". a(n) = the smallest product (the n-th binary palindrome)*(any binary palindrome) that is not a binary palindrome.

81, 25, 35, 81, 75, 289, 105, 81, 155, 1089, 135, 357, 315, 4225, 657, 425, 279, 1485, 321, 357, 635, 16641, 459, 825, 567, 5265, 657, 1155, 1275, 66049, 4641, 1485, 939, 1625, 1705, 1095, 1143, 10449, 1209, 1281, 1329, 2275, 1413, 1485, 2555, 263169

Offset

3,1

Comments

a(1) and a(2) are undefined, because the two first terms of A006995 are 0 and 1; and 0 times and 1 times any binary palindrome are binary palindromes, obviously.

Links

Michael S. Branicky, Table of n, a(n) for n = 3..10000

Formula

a(n) = A006995(n)*A175240(n).

Prog

(Python)
from itertools import count, islice, product
def is_bin_pal(n): return (b:=bin(n)[2:]) == b[::-1]
def bin_pals(): # generator of positive binary palindromes in base 10
    yield 1
    digits, midrange = 2, [[""], ["0", "1"]]
    for digits in count(2):
        for p in product("01", repeat=digits//2-1):
            left = "1"+"".join(p)
            for middle in midrange[digits%2]:
                yield int(left + middle + left[::-1], 2)
def agen(): # generator of terms
    g = bin_pals(); next(g)
    for n in count(3):
        bn = next(g)
        yield next(k*bn for k in bin_pals() if not is_bin_pal(k*bn))
print(list(islice(agen(), 46))) # Michael S. Branicky, Jan 09 2023

Crossrefs

Cf. A006995, A175240.

Sequence in context: A259687 A065793 A214104 * A178373 A147674 A033401

Adjacent sequences: A175238 A175239 A175240 * A175242 A175243 A175244

Keyword

base,look,nonn

Author

Leroy Quet, Mar 11 2010

Extensions

Extended by Ray Chandler, Mar 13 2010

Offset 3 from Michel Marcus, Jan 09 2023

Status

approved