If in a code language BADE = 1254 and HATE = 18520, then HEALER = ?

Let's find the logic by looking at the alphabet position numbers (A=1, B=2, C=3, ..., Z=26):
For BADE:

B = 2, A = 1, D = 4, E = 5

The given code is 1254.

Let's check the arrangement: The positions are rearranged. Specifically, the values are listed in alphabetical order of the letters?
Letters in BADE sorted alphabetically: A(1), B(2), D(4), E(5) ⟹ 1245 (not 1254).

Let's check another arrangement: 1, 2, 5, 4 corresponds to the positions of A(1), B(2), E(5), D(4). This means the letters are arranged as A-B-E-D.

For HATE:

H = 8, A = 1, T = 20, E = 5

The given code is 18520.

Notice that 1, 8, 5, 20 corresponds exactly to A(1), H(8), E(5), T(20).

Let's check what order A-B-E-D and A-H-E-T have in common:
In BADE, vowels are A, E and consonants are B, D. Arranged as Vowel 1, Consonant 1, Vowel 2, Consonant 2?
Let's look at alphabetical ordering of the letters:
For BADE: A(1), B(2), D(4), E(5). If we swap the last two: 1, 2, 5, 4.
For HATE: A(1), E(5), H(8), T(20). Alphabetical order is A(1), E(5), H(8), T(20) ⟹ 1, 5, 8, 20. The code given is 18520, which is A(1), H(8), E(5), T(20).

Let's look at another simple pattern: group by alphabetical order of vowels first, then consonants?
For BADE: Vowels = A(1), E(5). Consonants = B(2), D(4). Code is 1, 2, 5, 4. This doesn't separate vowels/consonants cleanly.

Let's look at the letter positions directly:
B(2), A(1), D(4), E(5) ⟹ swapped in pairs: (B,A) ⟹ A,B (1,2); (D,E) ⟹ E,D (5,4). Total code: 1254.
Let's check if this pair-swap holds for HATE:
(H,A) ⟹ A,H (1,8); (T,E) ⟹ E,T (5,20). Total code: 18520.
Yes! The pattern is to reverse the letters of every consecutive pair of the word, then write their normal position values.

Applying this pair-swap logic to HEALER:

Pair 1: HE ⟹ EH

Pair 2: AL ⟹ LA

Pair 3: ER ⟹ RE

Rearranged word: E H L A R E

Now substitute their numerical positions:

E = 5

H = 8

L = 12

A = 1

R = 18

E = 5

Combining these values sequentially gives: 58121185.