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

1,2

Comments

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

Links

Table of n, a(n) for n=1..40.

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

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

Example

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

Mathematica

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

Prog

(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

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).

Sequence in context: A018618 A294364 A108566 * A018416 A028909 A108567

Adjacent sequences: A057612 A057613 A057614 * A057616 A057617 A057618

Keyword

base,easy,nonn

Author

Henry Bottomley, Oct 09 2000

Status

approved