A358497 Replace each new digit in n with index 1, 2, ..., 9, 0 in order in which that digit appears in n, from left to right.

1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 12, 11, 12, 12, 12, 12, 12, 12, 12, 12, 12, 12, 11, 12, 12, 12, 12, 12, 12, 12, 12, 12, 12, 11, 12, 12, 12, 12, 12, 12, 12, 12, 12, 12, 11, 12, 12, 12, 12, 12, 12, 12, 12, 12, 12, 11, 12, 12, 12, 12, 12, 12, 12, 12, 12, 12, 11, 12

Offset

0,11

Comments

a(n) gives the canonical form which enumerates digits in order of their first occurrence in n, from left to right. a(n) uniquely defines the pattern of identical digits in n. - Dmytro Inosov, Jul 16 2024

Links

David A. Corneth, Table of n, a(n) for n = 0..9999

Formula

a(a(n)) = a(n). - Dmytro Inosov, Jul 16 2024

Example

n = 10 has 2 different digits; replace first encountered digit 1 -> 1, replace second digit 0 -> 2, therefore a(10) = 12.
n = 141 has 3 digits, but only 2 different ones; replace first encountered digit 1 -> 1, replace second encountered digit 4 -> 2, therefore a(141) = 121.

Mathematica

A358497[k_] := With[{pI = Values@PositionIndex@IntegerDigits@k}, MapIndexed[#1 -> Mod[#2[[1]], 10] &, pI, {2}] // Flatten // SparseArray // FromDigits]; (* Dmytro Inosov, Jul 15 2024 *)

Prog

(Python)
def A358497(n):
    d, s, k = dict(), str(n), 1
    for i in range(len(s)):
        if d.get(s[i], 0) == 0:
            d[s[i]] = str(k)
            k = (k + 1)%10
    s_t = list(s)
    for i in range(len(s)):s_t[i] = d[s[i]]
    return int(''.join(s_t))
print([A358497(i) for i in range(100)])
(Python)
def A358497(n):
    s, c, i  = str(n), {}, 49
    for d in map(ord, s):
        if d not in c:
            c[d] = i
            i += 1
    return int(s.translate(c)) # Chai Wah Wu, Jul 09 2024
(PARI) a(n) = {if(n == 0, return(1)); my(d = digits(n), m = Map(), t = 0); for(i = 1, #d, if(mapisdefined(m, d[i]), d[i] = mapget(m, d[i]) , t++; if(t == 10, t = 0); mapput(m, d[i], t); d[i] = t ) ); fromdigits(d) } \\ David A. Corneth, Nov 23 2022

Crossrefs

Cf. A071159, A227362, A358615 (record high values).

Sequence in context: A055123 A320636 A070560 * A019330 A086045 A072220

Adjacent sequences: A358494 A358495 A358496 * A358498 A358499 A358500

Keyword

nonn,base,easy

Author

Gleb Ivanov, Nov 19 2022

Status

approved