A345386 Non-palindromes whose largest proper divisor is a nontrivial (not a single-digit) palindrome.

110, 132, 154, 165, 176, 198, 231, 275, 297, 302, 322, 342, 362, 382, 385, 423, 453, 483, 504, 513, 524, 539, 543, 544, 564, 573, 584, 605, 655, 706, 726, 746, 755, 766, 786, 805, 847, 905, 908, 917, 928, 948, 955, 968, 988, 1010, 1029, 1030, 1050, 1057, 1059, 1070

Offset

1,1

Comments

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.

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.

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

Links

Karl-Heinz Hofmann, Table of n, a(n) for n = 1..10000

Example

The largest proper divisor of the non-palindrome 110 is a nontrivial palindrome 55. Thus, 110 is in this sequence.
The largest nontrivial divisor of the non-palindrome 143 is 13. Thus, though 143 is divisible by 11 it is not in this sequence.

Prog

(Python)
from sympy import divisors
def ispal(s): return s == s[::-1]
def ok(n):
    if ispal(str(n)): return False
    lpd = divisors(n)[-2]
    return lpd > 10 and ispal(str(lpd))
print(list(filter(ok, range(1060)))) # Michael S. Branicky, Jun 17 2021

Crossrefs

Cf. A075407.

Sequence in context: A244389 A176879 A039447 * A095611 A335272 A358255

Adjacent sequences: A345383 A345384 A345385 * A345387 A345388 A345389

Keyword

nonn,base

Author

Tanya Khovanova, Jun 17 2021

Status

approved