A175241 - OEIS

%I #21 Apr 20 2023 11:29:10

%S 81,25,35,81,75,289,105,81,155,1089,135,357,315,4225,657,425,279,1485,

%T 321,357,635,16641,459,825,567,5265,657,1155,1275,66049,4641,1485,939,

%U 1625,1705,1095,1143,10449,1209,1281,1329,2275,1413,1485,2555,263169

%N 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.

%C 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.

%H Michael S. Branicky, <a href="/A175241/b175241.txt">Table of n, a(n) for n = 3..10000</a>

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

%o (Python)

%o from itertools import count, islice, product

%o def is_bin_pal(n): return (b:=bin(n)[2:]) == b[::-1]

%o def bin_pals(): # generator of positive binary palindromes in base 10

%o     yield 1

%o     digits, midrange = 2, [[""], ["0", "1"]]

%o     for digits in count(2):

%o         for p in product("01", repeat=digits//2-1):

%o             left = "1"+"".join(p)

%o             for middle in midrange[digits%2]:

%o                 yield int(left + middle + left[::-1], 2)

%o def agen(): # generator of terms

%o     g = bin_pals(); next(g)

%o     for n in count(3):

%o         bn = next(g)

%o         yield next(k*bn for k in bin_pals() if not is_bin_pal(k*bn))

%o print(list(islice(agen(), 46))) # _Michael S. Branicky_, Jan 09 2023

%Y Cf. A006995, A175240.

%K base,look,nonn

%O 3,1

%A _Leroy Quet_, Mar 11 2010

%E Extended by _Ray Chandler_, Mar 13 2010

%E Offset 3 from _Michel Marcus_, Jan 09 2023