A164046 A001445 written in base 2.

11, 101, 1010, 10010, 100100, 1000100, 10001000, 100001000, 1000010000, 10000010000, 100000100000, 1000000100000, 10000001000000, 100000001000000, 1000000010000000, 10000000010000000, 100000000100000000, 1000000000100000000, 10000000001000000000

Offset: 1

Author

Jaroslav Krizek, Aug 08 2009

Keywords

• nonn
• base
• easy

Comments

The digit pattern is: one digit 1, A004526(n) times 0, one digit 1, and A004526(n-1) times 0.

Links

• G. C. Greubel, Table of n, a(n) for n = 1..995
• Index entries for linear recurrences with constant coefficients, signature (10,10,-100).

Programs

Mathematica

Table[IntegerString[(2^n + 2^(Floor[n/2]))/2, 2], {n, 2, 50}] (* G. C. Greubel, Sep 08 2017 *)
LinearRecurrence[{10,10,-100},{11,101,1010},30] (* Harvey P. Dale, Mar 06 2025 *)

Formula

a(n) = 2^n + 2^A004526(n-1) = A007088(A001445(n)).

From Chai Wah Wu, Sep 10 2020: (Start)

a(n) = 10*a(n-1) + 10*a(n-2) - 100*a(n-3) for n > 3.

G.f.: x*(-110*x^2 - 9*x + 11)/((10*x - 1)*(10*x^2 - 1)). (End)

Extensions

Extended by R. J. Mathar, Aug 11 2009