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
Dmytro S. Inosov and Emil Vlasák, Cryptarithmically unique terms in integer sequences, arXiv:2410.21427 [math.NT], 2024. See pp. 3, 18.
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
KEYWORD
nonn,base,easy
AUTHOR
Gleb Ivanov, Nov 19 2022
STATUS
approved