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A057615 ATS: Add Then Sort (i.e., double previous term and then sort digits). 17

%I #20 Jul 18 2021 02:07:49

%S 1,2,4,8,16,23,46,29,58,116,223,446,289,578,1156,1223,2446,2489,4789,

%T 5789,11578,12356,12247,24449,48889,77789,155578,111356,122227,244445,

%U 48889,77789,155578,111356,122227,244445,48889,77789,155578,111356

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

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

%H <a href="/index/Rec#order_06">Index entries for linear recurrences with constant coefficients</a>, signature (0,0,0,0,0,1).

%F 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

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

%t NestList[FromDigits[Sort[IntegerDigits[2#]]]&,1,40] (* _Harvey P. Dale_, Oct 03 2011 *)

%o (Python)

%o from itertools import accumulate

%o def ats(anm1, _): return int("".join(sorted(str(2*anm1))))

%o print(list(accumulate([1]*40, ats))) # _Michael S. Branicky_, Jul 17 2021

%Y Cf. A033861 for STA, A004000 for RATS.

%Y 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).

%K base,easy,nonn

%O 1,2

%A _Henry Bottomley_, Oct 09 2000

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Last modified March 29 03:41 EDT 2024. Contains 371264 sequences. (Running on oeis4.)