A069638 "Sorted" sum of two previous terms, beginning with 0,1. "Sorted" means to sort the digits of the sum in ascending order.

0, 1, 1, 2, 3, 5, 8, 13, 12, 25, 37, 26, 36, 26, 26, 25, 15, 4, 19, 23, 24, 47, 17, 46, 36, 28, 46, 47, 39, 68, 17, 58, 57, 115, 127, 224, 135, 359, 449, 88, 357, 445, 28, 347, 357, 47, 44, 19, 36, 55, 19, 47, 66, 113, 179, 229, 48, 277, 235, 125, 36, 116, 125, 124, 249, 337

Offset

0,4

Comments

The maximum value in this sequence is 667. After the 75th term, the next 120 terms (a(76) - a(195)) repeat as a group infinitely.

Links

Zak Seidov, Table of n, a(n) for n = 0..1000

Formula

a(n) = SORT[a(n-1) + a(n-2)].

Example

a(8)=12 because a(7)+a(6)=13+8=21 and the digits of 21 sorted in ascending order = 12.
Also a(17)=4 because a(16)+a(15)=15+25=40 and the digits of 40 sorted in ascending order = 04, or just 4;

Maple

a:= proc(n) option remember; `if`(n<2, n, parse(cat(
      sort(convert(a(n-1)+a(n-2), base, 10))[])))
    end:
seq(a(n), n=0..77);  # Alois P. Heinz, Aug 31 2022

Mathematica

a[0]:=0
a[1]:=1
a[n_] := a[n]=FromDigits[Sort[IntegerDigits[a[n-1]+a[n-2]]]] (* Peter J. C. Moses, Feb 08 2014 *)
nxt[{a_, b_}]:={b, FromDigits[Sort[IntegerDigits[a+b]]]}; NestList[nxt, {0, 1}, 70][[All, 1]] (* Harvey P. Dale, Jul 27 2020 *)

Prog

(Python)
a, terms = [0, 1], 66
[a.append(int("".join(sorted(str(a[-2]+a[-1]))))) for n in range(2, terms)]
print(a) # Michael S. Branicky, Aug 31 2022

Crossrefs

Cf. A000045, A001129, A004185, A237575, A237671.

Sequence in context: A267809 A010077 A065076 * A237568 A272918 A010076

Adjacent sequences: A069635 A069636 A069637 * A069639 A069640 A069641

Keyword

nonn,base

Author

Gil Broussard, Jan 16 2004

Status

approved