cp's OEIS Frontend

A104462 Convert the binary strings in A101305 to decimal.

%I A104462 #17 Jun 30 2022 08:40:46
%S A104462 0,2,20,328,10512,672800,86118464,22046326912,11287719379200,
%T A104462 11558624644301312,23672063271529088000,96960771160183144450048,
%U A104462 794302637344220319334797312,13013854410247705711981319168000,426437981314996820770203866497040384
%N A104462 Convert the binary strings in A101305 to decimal.
%C A104462 The a(n)-th composition in standard order is (2,3,..,n+1), where the k-th composition in standard order (graded reverse-lexicographic, A066099) is obtained by taking the set of positions of 1's in the reversed binary expansion of k, prepending 0, taking first differences, and reversing again. Moreover, the binary indices of a(n) are row n of A193973. Including 1 gives A164894, reverse A246534. - _Gus Wiseman_, Jun 28 2022
%H A104462 Michael S. Branicky, <a href="/A104462/b104462.txt">Table of n, a(n) for n = 0..80</a>
%e A104462 From _Gus Wiseman_, Jun 28 2022: (Start)
%e A104462 The terms together with their standard compositions begin:
%e A104462       0: ()
%e A104462       2: (2)
%e A104462      20: (2,3)
%e A104462     328: (2,3,4)
%e A104462   10512: (2,3,4,5)
%e A104462 (End)
%p A104462 convert(10,decimal,binary); convert(10100,decimal,binary); convert(101001000,decimal,binary); convert(10100100010000,decimal,binary); convert(10100100010000100000,decimal,binary);
%t A104462 stcinv[q_]:=Total[2^Accumulate[Reverse[q]]]/2;
%t A104462 Table[stcinv[Range[2,n]],{n,8}] (* _Gus Wiseman_, Jun 28 2022 *)
%o A104462 (Python)
%o A104462 def a(n): return 0 if n==0 else int("".join("1"+"0"*(i+1) for i in range(n)), 2)
%o A104462 print([a(n) for n in range(15)]) # _Michael S. Branicky_, Jun 28 2022
%Y A104462 Cf. A101305.
%Y A104462 A version for prime indices is A070826.
%Y A104462 Cf. A000120, A002110, A029931, A066099, A070939, A164894, A193973, A233564, A246534, A272919, A333218, A333255.
%K A104462 nonn,base
%O A104462 0,2
%A A104462 _Jorge Coveiro_, Apr 23 2005
%E A104462 a(14) and beyond from _Michael S. Branicky_, Jun 28 2022