A386552 Concatenate powers of 10.

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

Offset: 0

Author

Jason Bard, Jul 25 2025

Keywords

• nonn
• base
• easy

Comments

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

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

Links

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

Crossrefs

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

Programs

Maple

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

Mathematica

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

Python

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

Formula

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).