A046498 - OEIS

%I #14 Jun 09 2021 08:17:50

%S 6,9,66,99,333,363,393,636,666,696,939,969,999,3333,3663,3993,6336,

%T 6666,6996,9339,9669,9999,30303,30603,30903,33333,33633,33933,36363,

%U 36663,36963,39393,39693,39993,60306,60606,60906,63336,63636,63936

%N Palindromes expressible as the sum of 3 consecutive palindromes.

%H Michael S. Branicky, <a href="/A046498/b046498.txt">Table of n, a(n) for n = 1..15358</a> (all terms with <= 13 digits)

%H Patrick De Geest, <a href="http://www.worldofnumbers.com/index.html">World!Of Numbers</a>

%e 6666 = 2112 + 2222 + 2332.

%o (Python)

%o from itertools import product

%o def ispal(n): s = str(n); return s == s[::-1]

%o def pals(d, base=10): # all d-digit palindromes

%o   digits = "".join(str(i) for i in range(base))

%o   for p in product(digits, repeat=d//2):

%o     if d > 1 and p[0] == "0": continue

%o     left = "".join(p); right = left[::-1]

%o     for mid in [[""], digits][d%2]: yield int(left + mid + right)

%o def auptod(dd):

%o   alst  = [6, 9]

%o   last3 = [7, 8, 9]

%o   for d in range(2, dd+1):

%o     for p in pals(d):

%o       last3 = last3[1:] + [p]

%o       if ispal(sum(last3)): alst.append(sum(last3))

%o   return alst

%o print(auptod(5)) # _Michael S. Branicky_, Jun 09 2021

%Y Cf. A002113.

%K nonn,base

%O 1,1

%A _Patrick De Geest_, Sep 15 1998