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

Author

Gil Broussard, Jan 16 2004

Keywords

• nonn
• base

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.

Examples

			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;
		

Links

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

Crossrefs

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

Programs

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 *)

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

Formula

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