A065761 -id:A065761 - cp's OEIS frontend

A065447 Concatenation of 1, 00, 111, 0000, ..., n 1's (if n is odd) or n 0's (if n is even).

1, 100, 100111, 1001110000, 100111000011111, 100111000011111000000, 1001110000111110000001111111, 100111000011111000000111111100000000, 100111000011111000000111111100000000111111111, 1001110000111110000001111111000000001111111110000000000

Offset: 1

Lior Manor, Nov 18 2001

a(n) is divisible by A002275([(n+1)/2]) = (10^[(n+1)/2]-1)/9. Cf. A262806. - Max Alekseyev, Jun 02 2013

The unique sequence of binary words a(n) such that the k-th run of a(n) has length k, for k = 1..n . - Clark Kimberling, Mar 08 2024

			a(2) = 100, the concatenation of one 1, two 0's.
a(3) = 100111, the concatenation of one 1, two 0's, three 1's.
a(4) = 1001110000, the concatenation of one 1, two 0's, three 1's, four 0's.

Harry J. Smith, Table of n, a(n) for n = 1..44

For decimal version see A065760.

Cf. A000217, A065761, A371032.

a:= n-> parse(cat((irem(i,2)$i)$i=1..n)):
seq(a(n), n=1..10);  # Alois P. Heinz, Mar 08 2024

FoldList[Join, {1}, Map[ConstantArray[Mod[#, 2], #] &, Range[2, 10]]] (* Peter J. C. Moses, Mar 08 2024 *)

{ m=10; for (n=1, 44, if (n==1, a=1, m*=10; a*=m; if (n%2, a+=(m - 1)/9)); write("b065447.txt", n, " ", a) ) } \\ Harry J. Smith, Oct 19 2009

A065760 Concatenation of increasing number of alternating digits in base 2, starting with 1.

Original entry on oeis.org

1, 4, 39, 624, 19999, 1279936, 163831935, 41940975360, 21473779384831, 21989150090066944, 45033779384457103359, 184458360358736295358464, 1511082888058767731576545279, 24757582037954850514150117851136, 811256448219704541647671061746057215

Offset: 1

Lior Manor, Nov 18 2001

			a(5) = 19999 is formed by appending 1 five times (11111) to a(4) in base 2: 100111000011111.

Harry J. Smith, Table of n, a(n) for n = 1..50

Decimal version of A065447.

Cf. A065761.

a:= proc(n) option remember; `if`(n=1, 1,
      (t-> (a(n-1)+t)*2^n-t)(irem(n,2)))
    end:
seq(a(n), n=1..17);  # Alois P. Heinz, Mar 08 2024

With[{nn=20}, Table[FromDigits[Flatten[Take[Table[Table[If[EvenQ[n],0,1], {n}], {n,nn}], j]], 2], {j, nn}]] (* Harvey P. Dale, Sep 09 2012 *)

baseI(x, b)= { local(d, e=0, f=1); while (x>0, d=x-10*(x\10); x\=10; e+=d*f; f*=b); return(e) } { c=1; for (n=1, 50, if (n==1, a=1; b=1, c=c*10 + 1; if (n%2, d=c, d=0); b=b*10^n + d; a=baseI(b, 2)); write("b065760.txt", n, " ", a) ) } \\ Harry J. Smith, Oct 30 2009

a(n) = a(n-1) * 2^n if n is even, (a(n-1) + 1) * 2^n - 1 if n is odd. - Franklin T. Adams-Watters, Sep 18 2012

cp's OEIS Frontend

A065447 Concatenation of 1, 00, 111, 0000, ..., n 1's (if n is odd) or n 0's (if n is even).

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