Palindromic Day 28182

Palindromic properties of 28182 (showing only sequence members up to 40000):

A098834: palindromic Smith numbers.

4, 22, 121, 202, 454, 535, 636, 666, 1111, 1881, 3663, 7227, 7447, 9229, 10201, 17271, 22522, 24142, 28182, 33633, 38283

A Smith number is a composite number where the sum of its digits equals the sum of the digits of its prime factors. For 28182:$$ \begin{align} 28182 &\rightarrow 2+8+1+8+2 = 21 \\ 28182 &= 2 \times 3 \times 7 \times 11 \times 61\\ &\rightarrow 2 + 3 + 7 + 1+1+6 +1 =21 \end{align}$$

A046395: palindromes that are the product of 5 distinct primes.

6006, 8778, 20202, 28182

Here \(28182 = 2 \times 3 \times 7 \times 11 \times 61 \)

A099052: all palindromes of length > 1 in the decimal expansion of \(e\).

\(e\) = 2.71828182845904523536028747135266 ...

A045571: numbers that are palindromic, divisible by 11 and have an odd number of digits.

121, 242, 363, 484, 616, 737, 858, 979, 10901, 11011, 12221, 13431, 14641, 15851, 17171, 18381, 19591, 20702, 21912, 22022, 23232, 24442, 25652, 26862, 28182, 29392, 30503, 31713, 32923, 33033, 34243, 35453, 36663, 37873, 39193

All the palindromic numbers with an even number of digits are divisible by 11. The number of palindromic numbers with \(2k+1\) digits that are divisible by 11 is \((10^{k+1} + (-1)^k)/11\), and their asymptotic relative density within the set of all palindromic numbers with an odd number of digits is 1/11 (from OEIS comments).

A113838: palindromes sandwiched between twin primes.

4, 6, 282, 828, 858, 2112, 21012, 21612, 23832, 26262, 26862, 28182

Here of course the twin primes are 28181 and 28183.

A032751: palindromic Super-3 Numbers.

4554, 6776, 17471, 22322, 22722, 28182

Super-3 numbers \(n\) are of the form \(3 \times n^3 \) and contain three consecutive 3's.

Here \(3 \times 28182^3 = 67148557\textbf{333}704\)