# Numbers that are palindromes in N bases

## Mathematica, ~~80~~ 71 bytes

*Thanks to JungHwan Min for saving 9 bytes!*

```
Do[#!=Length[i~IntegerReverse~Range[2,i-2]~Cases~i]||Echo@i,{i,3,∞}]&
```

(`∞`

is the three-byte character U+221E.)
Pure function taking a nonnegative integer as input. `i~IntegerReverse~Range[2,i-2]`

creates a list of the reversals of the number `i`

in all the bases from `2`

to `i-2`

; then `Length[...~Cases~i]`

counts how many of these reversals are equal to `i`

again. `#!=...||Echo@i`

halts silently if that count is not equal to the input, and echoes `i`

if it is equal to the input. That procedure is embedded in a straightforward infinite loop.

## Jelly, ~~ 18 ~~ 15 bytes

-1 thanks to caird coinheringaahing.

```
ṄµbḊŒḂ€S’⁼³µ¡‘ß
```

**Try it online!** - the online interpreter will timeout at 60 seconds then flush it's output (unless it has a cached copy), offline it will print each in turn.

### How?

Evaluates numbers from `n`

up, printing them if they are in the sequence. Note that the first number in any output will be greater than `n`

since otherwise the range of `b`

is not great enough, so there is no need to seed the process with `3`

. Also note that the number of palindromes from base **2** to **x _{i}-2** inclusive is just one less than the number of palindromes from base

**2**to

**x**.

_{i}```
ṄµbḊŒḂ€S’⁼³µ¡‘ß - Main link: n
¡ - repeat...
Ṅ - ...action: print (the CURRENT n)
µ µ - ...number of times: this monadic chain:
Ḋ - deueue -> [2,3,4,...,n]
b - n converted to those bases
ŒḂ€ - is palindromic? for €ach
S - sum: counts the 1s
’ - decrement: throw away the truthy base n-1 one
⁼³ - equals input: Does this equal the ORIGINAL n?
‘ - increment n
ß - calls this link as a monad, with the incremented n.
```