A263451 - OEIS

%I #19 Sep 08 2022 08:46:14

%S 1,2,4,8,61,221,442,884,8761,75221,544210,8842100,87642100,875422100,

%T 8754421000,88754210000,877542100000,8755421000000,87542110000000,

%U 875422100000000,8754421000000000,88754210000000000,877542100000000000,8755421000000000000

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

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

%F a(n) >= A036447(n).

%F From _Alois P. Heinz_, Oct 19 2015: (Start)

%F G.f.: x*(99990000000*x^18 +86679000000*x^17 -333332100000*x^16 -13533210000*x^15 +6579000*x^14 +8577900*x^13 +354357900*x^12 +212157900*x^11 +60455790*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)).

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

%F a(n+1) = A004186(2*a(n)). - _Reinhard Zumkeller_, Oct 19 2015

%t s={1,2,4,8}; a=8; Do[b=FromDigits[Reverse[Sort[IntegerDigits[2*a]]]]; AppendTo[s,a=b],{20}]; s

%t NestList[FromDigits[ReverseSort[IntegerDigits[2 #]]]&,1,30] (* Requires Mathematica version 11 or later *) (* _Harvey P. Dale_, May 17 2019 *)

%o (Magma) [n eq 1 select 1 else Seqint(Sort(Intseq(2*Self(n-1)))): n in [1..30]]; // _Bruno Berselli_, Oct 19 2015

%o (Haskell)

%o a263451 n = a263451_list !! (n-1)

%o a263451_list = iterate (a004186 . (* 2)) 1

%o -- _Reinhard Zumkeller_, Oct 19 2015

%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 nonn,base,easy

%O 1,2

%A _Zak Seidov_, Oct 18 2015