A046498 Palindromes expressible as the sum of 3 consecutive palindromes.

6, 9, 66, 99, 333, 363, 393, 636, 666, 696, 939, 969, 999, 3333, 3663, 3993, 6336, 6666, 6996, 9339, 9669, 9999, 30303, 30603, 30903, 33333, 33633, 33933, 36363, 36663, 36963, 39393, 39693, 39993, 60306, 60606, 60906, 63336, 63636, 63936

Offset: 1

Author

Patrick De Geest, Sep 15 1998

Keywords

• nonn
• base

Examples

			6666 = 2112 + 2222 + 2332.
		

Links

• Michael S. Branicky, Table of n, a(n) for n = 1..15358 (all terms with <= 13 digits)
• Patrick De Geest, World!Of Numbers

Crossrefs

Cf. A002113.

Programs

Python

from itertools import product
def ispal(n): s = str(n); return s == s[::-1]
def pals(d, base=10): # all d-digit palindromes
  digits = "".join(str(i) for i in range(base))
  for p in product(digits, repeat=d//2):
    if d > 1 and p[0] == "0": continue
    left = "".join(p); right = left[::-1]
    for mid in [[""], digits][d%2]: yield int(left + mid + right)
def auptod(dd):
  alst  = [6, 9]
  last3 = [7, 8, 9]
  for d in range(2, dd+1):
    for p in pals(d):
      last3 = last3[1:] + [p]
      if ispal(sum(last3)): alst.append(sum(last3))
  return alst
print(auptod(5)) # Michael S. Branicky, Jun 09 2021