A136308 a(n) = (10^2^n - 1)/9.

1, 11, 1111, 11111111, 1111111111111111, 11111111111111111111111111111111, 1111111111111111111111111111111111111111111111111111111111111111

Offset: 0

Author

Ctibor O. Zizka, Mar 22 2008

Keywords

• base
• easy
• nonn

Comments

More generally, reading in base B >= 2: a(n) = (B^2^n - 1)/(B-1).

Recurrence: a(n) = a(n-1)*(B^K + 1) and a(0)=1 where K = floor(log_B a(n-1)) + 1.

B = 2 gives A051179; B = 3 gives A059918.

Crossrefs

Cf. A000042 (repunits).

In other bases: A051179, A059918.

Cf. A000079, A007088, A007089, A007953.

Programs

Magma

A136308 := func; [A136308(n):n in[0..7]];

Mathematica

(10^2^Range[0, 10] - 1)/9 (* G. C. Greubel, Apr 19 2021 *)

Sage

[(10^2^n -1)/9 for n in (0..10)] # G. C. Greubel, Apr 19 2021

Formula

a(n) = a(n-1)*(10^K + 1) and a(0)=1 where K=floor(log_10 a(n-1)) + 1 = 2^n + 1.

a(n) = A000042(A000079(n)) = A007088(A051179(n)) = A007089(A059918(n)).

A007953(a(n)) = 2^n. - Stefano Spezia, Mar 27 2025

Extensions

Edited by Jason Kimberley, Dec 18 2012