A028570 Numbers k such that k*(k + 9) is a palindrome.

0, 2, 12, 44, 137, 157, 167, 248, 258, 1639, 1664, 1694, 5392, 15904, 16997, 160187, 487619, 1547147, 14674184, 14790532, 15019614, 15336644, 25234083, 26132578, 26211438, 26216753, 48675319, 49407017, 52030352, 54072524, 151698472, 164399727, 497665874

Offset: 1

Author

Patrick De Geest

Keywords

• nonn
• base

Links

• Michael S. Branicky, Table of n, a(n) for n = 1..42
• Patrick De Geest, Palindromic Quasipronics of the form n(n+x)
• Erich Friedman, What's Special About This Number? (See entries 258, 1664.)

Crossrefs

Cf. A028569, A028571.

Programs

Magma

f:=func; [k:k in [0..2*10^7]| f(k*(k+9))]; // Marius A. Burtea, Nov 11 2019

Mathematica

Select[Range[0, 9999], PalindromeQ[#^2 + 9#] &] (* Alonso del Arte, Nov 10 2019 *)

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+9)):
            yield k
print(list(islice(agen(), 18))) # Michael S. Branicky, Jan 25 2022

Scala

def palQ(n: Int, b: Int = 10): Boolean = n - Integer.parseInt(n.toString.reverse) == 0
(0 to 9999).filter((n: Int) => palQ(n * n + 9 * n)) // Alonso del Arte, Nov 10 2019

Extensions

a(27) and beyond from Michael S. Branicky, Jan 25 2022