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

Author

Ctibor O. Zizka, Jul 13 2021

Keywords

• nonn
• base
• easy

Examples

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

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).

Crossrefs

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

Programs

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 *)

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

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