A101305 -id:A101305 - cp's OEIS frontend

A104462 Convert the binary strings in A101305 to decimal.

0, 2, 20, 328, 10512, 672800, 86118464, 22046326912, 11287719379200, 11558624644301312, 23672063271529088000, 96960771160183144450048, 794302637344220319334797312, 13013854410247705711981319168000, 426437981314996820770203866497040384

Offset: 0

Jorge Coveiro, Apr 23 2005

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

			From _Gus Wiseman_, Jun 28 2022: (Start)
The terms together with their standard compositions begin:
      0: ()
      2: (2)
     20: (2,3)
    328: (2,3,4)
  10512: (2,3,4,5)
(End)

Michael S. Branicky, Table of n, a(n) for n = 0..80

Cf. A101305.
A version for prime indices is A070826.
Cf. A000120, A002110, A029931, A066099, A070939, A164894, A193973, A233564, A246534, A272919, A333218, A333255.

convert(10,decimal,binary); convert(10100,decimal,binary); convert(101001000,decimal,binary); convert(10100100010000,decimal,binary); convert(10100100010000100000,decimal,binary);

stcinv[q_]:=Total[2^Accumulate[Reverse[q]]]/2;
Table[stcinv[Range[2,n]],{n,8}] (* Gus Wiseman, Jun 28 2022 *)

def a(n): return 0 if n==0 else int("".join("1"+"0"*(i+1) for i in range(n)), 2)
print([a(n) for n in range(15)]) # Michael S. Branicky, Jun 28 2022

a(14) and beyond from Michael S. Branicky, Jun 28 2022

A386552 Concatenate powers of 10.

Original entry on oeis.org

1, 110, 110100, 1101001000, 110100100010000, 110100100010000100000, 1101001000100001000001000000, 110100100010000100000100000010000000, 110100100010000100000100000010000000100000000, 1101001000100001000001000000100000001000000001000000000

Offset: 0

Jason Bard, Jul 25 2025

Binary version of A045507. Base-2 representation of A164894.

Concatenate first A000217(n+1) terms of A010054.

Jason Bard, Table of n, a(n) for n = 0..43

Cf. A000096, A000217, A010054, A011557, A045507, A051639, A101305, A133082, A164894, A242646.

a:= proc(n) option remember;
      `if`(n<0, 0, parse(cat(a(n-1), 10^n)))
    end:
seq(a(n), n=0..10);  # Alois P. Heinz, Jul 28 2025

a[0] = 1; a[n_] := a[n - 1]*10^(n+1) + 10^n; Table[a[n], {n, 0, 9}]

def A386552(n): return 10**n*sum(10**(k*((n<<1)-k+1)>>1) for k in range(n+1)) # Chai Wah Wu, Aug 05 2025

a(n) = Sum_{k=1..n+1} 10^A133082(k,n+2).
a(n) = A101305(n) + 10^A000096(n).
For n >= 1, a(n) = 10^(n+1)*a(n-1)+10^n.
Number of digits in a(n) is A000217(n+1).

cp's OEIS Frontend

A104462 Convert the binary strings in A101305 to decimal.

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