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A346296 a(0) = 1; thereafter a(n) = 2*a(n-1) + 1, with digits rearranged into nondecreasing order.

%I A346296 #66 Oct 01 2023 13:13:05
%S A346296 1,3,7,15,13,27,55,111,223,447,589,1179,2359,1479,2599,1599,1399,2799,
%T A346296 5599,11199,22399,44799,58999,117999,235999,147999,259999,159999,
%U A346296 139999,279999,559999,1119999,2239999,4479999,5899999,11799999,23599999,14799999,25999999
%N A346296 a(0) = 1; thereafter a(n) = 2*a(n-1) + 1, with digits rearranged into nondecreasing order.
%H A346296 Harvey P. Dale, <a href="/A346296/b346296.txt">Table of n, a(n) for n = 0..1000</a>
%H A346296 <a href="/index/Rec#order_13">Index entries for linear recurrences with constant coefficients</a>, signature (1,0,0,0,0,0,0,0,0,0,0,100,-100).
%F A346296 a(n) = A004185(2*a(n-1)+1).
%F A346296 For k >= 1;
%F A346296 a(12*k-9) = 100^(k-1) *   16 - 1;
%F A346296 a(12*k-8) = 100^(k-1) *   14 - 1;
%F A346296 a(12*k-7) = 100^(k-1) *   28 - 1;
%F A346296 a(12*k-6) = 100^(k-1) *   56 - 1;
%F A346296 a(12*k-5) = 100^(k-1) *  112 - 1;
%F A346296 a(12*k-4) = 100^(k-1) *  224 - 1;
%F A346296 a(12*k-3) = 100^(k-1) *  448 - 1;
%F A346296 a(12*k-2) = 100^(k-1) *  590 - 1;
%F A346296 a(12*k-1) = 100^(k-1) * 1180 - 1;
%F A346296 a(12*k)   = 100^(k-1) * 2360 - 1;
%F A346296 a(12*k+1) = 100^(k-1) * 1480 - 1;
%F A346296 a(12*k+2) = 100^(k-1) * 2600 - 1.
%F A346296 G.f.: -(1800*x^15 -720*x^14 +1080*x^13 -1080*x^12 -590*x^11 -142*x^10 -224*x^9 -112*x^8 -56*x^7 -28*x^6 -14*x^5 +2*x^4 -8*x^3 -4*x^2 -2*x -1) / ((x-1)*(10*x^6-1)*(10*x^6+1)). - _Alois P. Heinz_, Aug 02 2021
%F A346296 a(n) = 100*a(n-12) + 99 for n >= 15. - _Pontus von Brömssen_, Sep 01 2021
%e A346296 a(3) = A004185(2*7+1) = A004185(15) = 15.
%e A346296 a(4) = A004185(2*15+1) = A004185(31) = 13.
%t A346296 a[0] = 1; a[n_] := a[n] = FromDigits @ Sort @ IntegerDigits[2*a[n - 1] + 1]; Array[a, 45, 0] (* _Amiram Eldar_, Jul 13 2021 *)
%t A346296 NestList[FromDigits[Sort[IntegerDigits[2#+1]]]&,1,40] (* _Harvey P. Dale_, Oct 01 2023 *)
%o A346296 (PARI) lista(nn) = {my(va = vector(nn)); va[1] = 1; for (n=2, nn, va[n] = fromdigits(vecsort(digits(2*va[n-1]+1)));); va;} \\ _Michel Marcus_, Aug 31 2021
%o A346296 (Python)
%o A346296 from itertools import accumulate
%o A346296 def atis(anm1, _): return int("".join(sorted(str(2*anm1+1))))
%o A346296 print(list(accumulate([1]*39, atis))) # _Michael S. Branicky_, Aug 31 2021
%Y A346296 Cf. A004185, A010888, A057615, A069638, A321542.
%K A346296 nonn,base,easy
%O A346296 0,2
%A A346296 _Ctibor O. Zizka_, Jul 13 2021