A235775 a(n) = A047842(A047842(n)), say what you see, once repeated.

1011, 21, 1112, 1113, 1114, 1115, 1116, 1117, 1118, 1119, 1031, 1112, 3112, 3113, 3114, 3115, 3116, 3117, 3118, 3119, 102112, 3112, 22, 211213, 211214, 211215, 211216, 211217, 211218, 211219, 102113, 3113, 211213, 1213, 211314, 211315, 211316, 211317, 211318

Offset: 0

Author

Reinhard Zumkeller, Jan 15 2014

Keywords

• nonn
• base

Comments

a(n) does not depend on the order of digits of n, a property inherited from A047842. - M. F. Hasler, Jan 11 2024

Examples

			a(10) = A047842(1011) = 1031;
a(11) = A047842(21) = 1112;
a(12) = A047842(1112) = 3112;
a(100) = A047842(2011) = 102112;
a(101) = A047842(1021) = 102112;
a(102) = A047842(101112) = 104112.
For n = 20231231, digits of the date 2023-12-31, a(n) = 10213223 = A047842(n) because this is a fixed point of A047842. Since the order of the digits of n does not matter and there are no leading zeros, this holds also for the numbers resulting from notation dd.mm.yyyy or mm/dd/yyyy. - _M. F. Hasler_, Jan 11 2024
		

Links

• Reinhard Zumkeller, Table of n, a(n) for n = 0..10000

Crossrefs

Cf. A047842, A328447.

Programs

Haskell

a235775 = a047842 . a047842

PARI

A235775(n) = A047842(A047842(n)) \\ M. F. Hasler, Jan 11 2024

Python

def A235775(n):
    s = str(n)
    s = ''.join(str(s.count(d))+d for d in sorted(set(s)))
    return int(''.join(str(s.count(d))+d for d in sorted(set(s)))) # Chai Wah Wu, Feb 12 2023

Formula

From M. F. Hasler, Jan 11 2024: (Start)

a(n) = a(A328447(n)) = a(m) for all n and all m having the same digits as n, considering their respective multiplicity.

a(n) = A047842(n) =: m iff m is a fixed point of A047842. (End)