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

1,1

Links

Michael S. Branicky, Table of n, a(n) for n = 1..15358 (all terms with <= 13 digits)

Patrick De Geest, World!Of Numbers

Example

6666 = 2112 + 2222 + 2332.

Prog

(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

Crossrefs

Cf. A002113.

Sequence in context: A359800 A264380 A284636 * A119738 A299917 A204383

Adjacent sequences: A046495 A046496 A046497 * A046499 A046500 A046501

Keyword

nonn,base

Author

Patrick De Geest, Sep 15 1998

Status

approved