A346221 Palindromes that are multiples of 11 and whose digit sum is also a multiple of 11.

2992, 3883, 4774, 5665, 6556, 7447, 8338, 9229, 10901, 20702, 30503, 40304, 50105, 70807, 80608, 90409, 119911, 128821, 137731, 146641, 155551, 164461, 173371, 182281, 191191, 209902, 218812, 227722, 236632, 245542, 254452, 263362, 272272, 281182, 290092, 308803

Offset

1,1

Comments

Palindromes in A216995.

Links

Table of n, a(n) for n=1..36.

Example

11 is a palindrome that is a multiple of 11, but its digit sum is not divisible by 11. Thus, 11 is not in this sequence.

Mathematica

Select[Range[400000], PalindromeQ[#] && IntegerQ[#/11] && IntegerQ[Total[IntegerDigits[#]]/11] &]

Prog

(Python)
from itertools import product
def sd(n): return sum(map(int, str(n)))
def pals(d, base=10): # all positive 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]:
            t = int(left + mid + right)
            if t > 0: yield t
def ok(pal): return pal%11 == 0 and sd(pal)%11 == 0
print([p for d in range(1, 7) for p in pals(d) if ok(p)]) # Michael S. Branicky, Jul 11 2021
(PARI) isok(m) = my(d=digits(m)); (Vecrev(d) == d) && !(m % 11) && !(vecsum(d) % 11); \\ Michel Marcus, Aug 06 2021

Crossrefs

Cf. A002113, A083513, A166311 (halves of even length terms), A216995.

Sequence in context: A221725 A205241 A317398 * A253962 A253955 A253758

Adjacent sequences: A346218 A346219 A346220 * A346222 A346223 A346224

Keyword

nonn,base

Author

Tanya Khovanova, Jul 11 2021

Status

approved