# All your base palindromic belong to us

### Pyth, 13 bytes

```
mlf_ITjLdSdSQ
```

The brevity of this is mostly due to the `I`

nvaluable "`I`

nvariant" command.

```
msf_ITjLdSdSQ implicit: Q=input
m d map lambda d over
SQ Inclusive range 1 to Q
jLdSd Convert d to all the bases between 1 and d
f filter lambda T:
_IT is invariant under reverse
l number that are invariant under reverse
```

If `True`

is an acceptable output for `1`

, `msm_IjdkSdSQ`

(12 bytes) works.

Try it here.

## Jelly, 14 bytes

```
bR‘$µ=UP€S
RÇ€
```

Try it online!

### Non-competing version

The Jelly interpreter had a bug that made converting to unary impossible. This has been fixed now, so the following code (**12 bytes**) also accomplishes the task at hand.

```
bRµ=UP€S
RÇ€
```

Try it online!

### How it works

```
bR‘$µ=UP€S Helper link. Argument: z
R‘$ Apply range and increment, i.e., map z to [2, ..., z + 1].
In the non-competing version R simply maps z to [1, ... z].
b Convert z to each of the bases to the right.
µ Begin a new, monadic chain. Argument: base conversions
=U Compare the digits of each base with the reversed digits.
= has depth 0, so [1,2,3]=[1,3,3] yields [1,0,1].
P€ Take the product of the innermost arrays.
S Sum all resulting Booleans.
RÇ€ Main link. Argument: n
R Yield [1, ..., n].
Ç€ Apply the helper link to each.
```

## MATL, 19 ~~20~~ bytes

```
:"[email protected]:Q"[email protected]:YAtP=A+
```

Uses current release (10.1.0), which is earlier than this challenge.

**Try it online**!

### Explanation

```
: % vector [1,2,...,N], where "N" is implicit input
" % for each number in that vector
0 % push 0
@ % push number 1,2,...N corresponding to current iteration, say "n"
XK % copy n to clipboard
:Q % vector [2,3,...,n+1]
" % for each number "m" in that vector
K % push n
@: % vector [1,2,...,m]
YA % express n in base m with symbols 1,2,...,m
tP % duplicate and permute
=A % 1 if all entries are equal (palindrome), 0 otherwise
+ % add that number
% implicitly close the two loops and display stack contents
```