A263451 a(n) is the largest anagram of 2*a(n-1), a(1)=1.

1, 2, 4, 8, 61, 221, 442, 884, 8761, 75221, 544210, 8842100, 87642100, 875422100, 8754421000, 88754210000, 877542100000, 8755421000000, 87542110000000, 875422100000000, 8754421000000000, 88754210000000000, 877542100000000000, 8755421000000000000

Offset: 1

Author

Zak Seidov, Oct 18 2015

Keywords

• nonn
• base
• easy

Comments

For large n, a(n)/a(n-1) ~ 10.

Crossrefs

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).

Programs

Haskell

a263451 n = a263451_list !! (n-1)
a263451_list = iterate (a004186 . (* 2)) 1
-- Reinhard Zumkeller, Oct 19 2015

Magma

[n eq 1 select 1 else Seqint(Sort(Intseq(2*Self(n-1)))): n in [1..30]]; // Bruno Berselli, Oct 19 2015

Mathematica

s={1,2,4,8}; a=8; Do[b=FromDigits[Reverse[Sort[IntegerDigits[2*a]]]]; AppendTo[s,a=b],{20}]; s
NestList[FromDigits[ReverseSort[IntegerDigits[2 #]]]&,1,30] (* Requires Mathematica version 11 or later *) (* Harvey P. Dale, May 17 2019 *)

Formula

a(n) >= A036447(n).

From Alois P. Heinz, Oct 19 2015: (Start)

G.f.: x*(99990000000*x^18 [phone]*x^17 -333332100000*x^16 -13533210000*x^15 +6579000*x^14 +8577900*x^13 [phone]*x^12 [phone]*x^11 [phone]*x^10 +7924779*x^9 +3991239*x^8 +1999116*x^7 +999558*x^6 -221*x^5 -61*x^4 -8*x^3 -4*x^2 -2*x -1) / ((10*x-1) *(1+10*x) *(100*x^2+10*x+1) *(100*x^2-10*x+1)).

a(n) = 10^6 * a(n-6) for n >= 20. (End)

a(n+1) = A004186(2*a(n)). - Reinhard Zumkeller, Oct 19 2015