Pademi - a new type of number sequence

I have discovered many different number sequences made up of numbers with peculiar properties. By getting to know quite a few of them (deficient, perfect, abundant, evil, weird, palindrome, prime, etc), I found my way to a new mix of properties. As with other such sequences, they don’t neccessary have a greater purpose, but rather a recreational one.

I wrote a script in Python that looked for numbers below with these qualities, odd as they are (not really, that’s a pun):

1. Has an equal number of 0’s and 1’s in its binary form
2. Is a palindrome number in its binary form
3. A deficient number in decimal form.

I found 14 such numbers below 10 000:

9, 153, 165, 195, 2289, 2409, 2457, 2661, 2709, 2829, 3171, 3219, 3339, 3591

For instance, 2289 has equal number of 1’s and 0’s in base 2, where it also is a palindrome: 100011110001, and is deficient in base 10, which means that the sum of its proper divisors is less than the number 2289.

So, what do I call these numbers?

• Equal-palindrome-deficient?
• Twin-bits-lesser-palindrome?
• Mirrored-deficient-palindrome?
• Deficient-twinbit-palindrome?
• Mirrored-deficiant-twinbits

Not really sure here, it should be a simpler name. Weird is already taken, which would fit this pretty well I think. What if I pick a couple of letters from each in Mirrored-Deficient-Palindrome, MiDePa or PaDeMi…

Pademi numbers?

Lets go with that.