A057615 ATS: Add Then Sort (i.e., double previous term and then sort digits).

1, 2, 4, 8, 16, 23, 46, 29, 58, 116, 223, 446, 289, 578, 1156, 1223, 2446, 2489, 4789, 5789, 11578, 12356, 12247, 24449, 48889, 77789, 155578, 111356, 122227, 244445, 48889, 77789, 155578, 111356, 122227, 244445, 48889, 77789, 155578, 111356

Offset: 1

Author

Henry Bottomley, Oct 09 2000

Keywords

• base
• easy
• nonn

Comments

Starting from a(1)=1 sequence cycles starting from a(25) = 48889, 77789, 155578, 111356, 122227, 244445, 48889, ... etc.

Examples

			a(8)=29 since a(7)=46, 46 + 46 = 92 and 92 sorted is 29.
		

Links

• Index entries for linear recurrences with constant coefficients, signature (0,0,0,0,0,1).

Crossrefs

Cf. A033861 for STA, A004000 for RATS.

The following are parallel families: A000079 (2^n), A004094 (2^n reversed), A028909 (2^n sorted up), A028910 (2^n sorted down), A036447 (double and reverse), A057615 (double and sort up), A263451 (double and sort down); A000244 (3^n), A004167 (3^n reversed), A321540 (3^n sorted up), A321539 (3^n sorted down), A163632 (triple and reverse), A321542 (triple and sort up), A321541 (triple and sort down).

Programs

Mathematica

NestList[FromDigits[Sort[IntegerDigits[2#]]]&,1,40] (* Harvey P. Dale, Oct 03 2011 *)

Python

from itertools import accumulate
def ats(anm1, _): return int("".join(sorted(str(2*anm1))))
print(list(accumulate([1]*40, ats))) # Michael S. Branicky, Jul 17 2021

Formula

G.f.: x*(-219996*x^29 - 109980*x^28 - 99000*x^27 - 144000*x^26 - 72000*x^25 - 44100*x^24 - 21960*x^23 - 9801*x^22 - 11133*x^21 - 10422*x^20 - 5211*x^19 - 4500*x^18 - 2043*x^17 - 2223*x^16 - 1107*x^15 - 1098*x^14 - 549*x^13 - 243*x^12 - 423*x^11 - 207*x^10 - 108*x^9 - 54*x^8 - 27*x^7 - 45*x^6 - 23*x^5 - 16*x^4 - 8*x^3 - 4*x^2 - 2*x - 1)/(x^6 - 1). - Chai Wah Wu, Nov 20 2018