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

1,2

Links

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

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 *)

Prog

(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

Crossrefs

Cf. A002113, A109883.

Sequence in context: A274124 A045910 A128290 * A232709 A249334 A338257

Adjacent sequences: A109999 A110000 A110001 * A110003 A110004 A110005

Keyword

base,nonn

Author

Jason Earls, Sep 02 2005

Extensions

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

Status

approved