A028567 Numbers k such that k*(k+8) is a palindrome.

0, 1, 3, 66, 88, 91, 173, 216, 225, 284, 294, 696, 707, 924, 2235, 2828, 6996, 9394, 28314, 30031, 57489, 69996, 93844, 188583, 228175, 241097, 283778, 298144, 597883, 699996, 896478, 1934063, 2281817, 6999996, 7243225, 17646619, 17869169, 19782199, 23352327

Offset: 1

Author

Patrick De Geest

Keywords

• nonn
• base

Comments

For i >= 0, 69^i6 is a term with corresponding palindrome 48(99)^{2*i}84, where ^ is repeated concatenation. - Michael S. Branicky, Jan 24 2022

Links

• Michael S. Branicky, Table of n, a(n) for n = 1..58
• Patrick De Geest, Palindromic Quasipronics of the form n(n+x)
• Erich Friedman, What's Special About This Number? (See entries 696, 2235, 2828, 6996, 9394.)

Programs

Mathematica

Select[Range[0,8*10^6],PalindromeQ[#(#+8)]&] (* Requires Mathematica version 10 or later *) (* Harvey P. Dale, May 28 2017 *)

Python

from itertools import count, islice
def ispal(n): s = str(n); return s == s[::-1]
def agen():
    for k in count(0):
        if ispal(k*(k+8)):
            yield k
print(list(islice(agen(), 35))) # Michael S. Branicky, Jan 24 2022

Extensions

a(36) and beyond from Michael S. Branicky, Jan 24 2022