A396231 Sort digits in descending order then add to original number, repeat, starting with 1.

1, 2, 4, 8, 16, 77, 154, 695, 1660, 8270, 16990, 116600, 777700, 1555400, 7109500, 16860500, 103511500, 656622500, 1323174700, 9066495800, 19053149800, 118907460800, 1107671570800, 9885322680800, 19774188002800, 118661930112800, 1107325141223800, 9861657362334800

Offset

1,2

Links

Michael S. Branicky, Table of n, a(n) for n = 1..1012

Formula

a(n+1) = a(n) + A004186(a(n)), a(1) = 1. - Michael S. Branicky, May 21 2026

Example

Start with first term 1, sort in descending order and add to 1, 1+1 = 2 (second term is 2).
Repeat: 2+2 = 4, 4+4 = 8, 8+8 = 16, 16+61 = 77, 77+77 = 154, 154+541 = 695 and so on.

Mathematica

NestList[#+FromDigits[Reverse[Sort[IntegerDigits[#]]]] &, 1, 27] (* Stefano Spezia, May 20 2026 *)

Prog

(Python)
from itertools import islice
def agen(): # generator of terms
    an = 1
    while True:
        yield an
        an += int("".join(sorted(str(an), reverse=True)))
print(list(islice(agen(), 28))) # Michael S. Branicky, May 21 2026

Crossrefs

Cf. A004186, A033860 (same for ascending order).

Sequence in context: A001127 A374734 A051299 * A097049 A119490 A013174

Adjacent sequences: A396227 A396228 A396230 * A396232 A396233 A396234

Keyword

nonn,base,easy

Author

Dave Durgin, May 19 2026

Extensions

More terms from Michael S. Branicky, May 21 2026

Status

approved