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

1, 3, 7, 15, 13, 27, 55, 111, 223, 447, 589, 1179, 2359, 1479, 2599, 1599, 1399, 2799, 5599, 11199, 22399, 44799, 58999, 117999, 235999, 147999, 259999, 159999, 139999, 279999, 559999, 1119999, 2239999, 4479999, 5899999, 11799999, 23599999, 14799999, 25999999

Offset

0,2

Links

Harvey P. Dale, Table of n, a(n) for n = 0..1000

Index entries for linear recurrences with constant coefficients, signature (1,0,0,0,0,0,0,0,0,0,0,100,-100).

Formula

a(n) = A004185(2*a(n-1)+1).

For k >= 1;

a(12*k-9) = 100^(k-1) * 16 - 1;

a(12*k-8) = 100^(k-1) * 14 - 1;

a(12*k-7) = 100^(k-1) * 28 - 1;

a(12*k-6) = 100^(k-1) * 56 - 1;

a(12*k-5) = 100^(k-1) * 112 - 1;

a(12*k-4) = 100^(k-1) * 224 - 1;

a(12*k-3) = 100^(k-1) * 448 - 1;

a(12*k-2) = 100^(k-1) * 590 - 1;

a(12*k-1) = 100^(k-1) * 1180 - 1;

a(12*k) = 100^(k-1) * 2360 - 1;

a(12*k+1) = 100^(k-1) * 1480 - 1;

a(12*k+2) = 100^(k-1) * 2600 - 1.

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

a(n) = 100*a(n-12) + 99 for n >= 15. - Pontus von Brömssen, Sep 01 2021

Example

a(3) = A004185(2*7+1) = A004185(15) = 15.
a(4) = A004185(2*15+1) = A004185(31) = 13.

Mathematica

a[0] = 1; a[n_] := a[n] = FromDigits @ Sort @ IntegerDigits[2*a[n - 1] + 1]; Array[a, 45, 0] (* Amiram Eldar, Jul 13 2021 *)
NestList[FromDigits[Sort[IntegerDigits[2#+1]]]&, 1, 40] (* Harvey P. Dale, Oct 01 2023 *)

Prog

(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
(Python)
from itertools import accumulate
def atis(anm1, _): return int("".join(sorted(str(2*anm1+1))))
print(list(accumulate([1]*39, atis))) # Michael S. Branicky, Aug 31 2021

Crossrefs

Cf. A004185, A010888, A057615, A069638, A321542.

Sequence in context: A334782 A102032 A086517 * A332374 A152677 A135374

Adjacent sequences: A346293 A346294 A346295 * A346297 A346298 A346299

Keyword

nonn,base,easy

Author

Ctibor O. Zizka, Jul 13 2021

Status

approved