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

Author

Tanya Khovanova, Jul 11 2021

Keywords

• nonn
• base

Comments

Palindromes in A216995.

Examples

			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.
		

Crossrefs

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

Programs

Mathematica

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

PARI

isok(m) = my(d=digits(m)); (Vecrev(d) == d) && !(m % 11) && !(vecsum(d) % 11); \\ Michel Marcus, Aug 06 2021

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