A345386 - OEIS

%I #18 Jun 19 2021 08:38:01

%S 110,132,154,165,176,198,231,275,297,302,322,342,362,382,385,423,453,

%T 483,504,513,524,539,543,544,564,573,584,605,655,706,726,746,755,766,

%U 786,805,847,905,908,917,928,948,955,968,988,1010,1029,1030,1050,1057,1059,1070

%N Non-palindromes whose largest proper divisor is a nontrivial (not a single-digit) palindrome.

%C Contains A075407 (Non-palindromic numbers such that the largest proper divisor is a palindrome having at least two digits and no other divisor is a palindrome with at least two digits) as a subsequence.

%C Two-digit numbers divisible by nontrivial palindromes are divisible by 11 and are palindromes themselves. Thus, the smallest number in this sequence has at least three digits.

%C The first nine terms are divisible by 11, but the tenth term (302) is not. Its largest proper divisor is 151.

%H Karl-Heinz Hofmann, <a href="/A345386/b345386.txt">Table of n, a(n) for n = 1..10000</a>

%e The largest proper divisor of the non-palindrome 110 is a nontrivial palindrome 55. Thus, 110 is in this sequence.

%e The largest nontrivial divisor of the non-palindrome 143 is 13. Thus, though 143 is divisible by 11 it is not in this sequence.

%o (Python)

%o from sympy import divisors

%o def ispal(s): return s == s[::-1]

%o def ok(n):

%o     if ispal(str(n)): return False

%o     lpd = divisors(n)[-2]

%o     return lpd > 10 and ispal(str(lpd))

%o print(list(filter(ok, range(1060)))) # _Michael S. Branicky_, Jun 17 2021

%Y Cf. A075407.

%K nonn,base

%O 1,1

%A _Tanya Khovanova_, Jun 17 2021