A110002 Palindromes whose perfect deficiency (A109883) is also palindromic.

1, 2, 3, 4, 5, 6, 7, 8, 9, 22, 44, 222, 292, 414, 646, 717, 848, 979, 27072, 28882, 45954, 74247, 90109, 96569, 118811, 2376732, 5136315, 5185815, 5266625, 5635365, 5684865, 6344436, 7424247, 7481847, 7484847, 7929297, 9858589, 12333321, 21922912, 32255223

Offset: 1

Author

Jason Earls, Sep 02 2005

Keywords

• base
• nonn

Links

• Michael S. Branicky, Table of n, a(n) for n = 1..101 (all terms < 10^14)

Crossrefs

Cf. A002113, A109883.

Programs

Mathematica

subtract = If[ #1 < #2, Throw[ #1], #1 - #2]&;d[n_] := Catch @ Fold[subtract, n, Divisors @ n];Select[Range[10000000],PalindromeQ[#]&&PalindromeQ[d[#]]&] (* James C. McMahon, Mar 31 2024 *)

Python

# uses imports, function in A109883
from itertools import count, islice, product
def ispal(n): return (s:=str(n)) == s[::-1]
def pals(): # generator of palindromes
    digits = "0123456789"
    yield from map(int, digits)
    for d in count(2):
        for f in "123456789":
            for p in product(digits, repeat=d//2-1):
                left = f + "".join(p); right = left[::-1]
                for mid in [[""], digits][d%2]:
                    yield int(left + mid + right)
def agen(): yield from (p for p in pals() if p>0 and ispal(A109883(p)))
print(list(islice(agen(), 40))) # Michael S. Branicky, Mar 31 2024

Extensions

a(38) and beyond from Michael S. Branicky, Mar 31 2024