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

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

Offset: 1

Author

Lior Manor, Nov 18 2001

Keywords

• base
• easy
• nonn

Examples

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

Links

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

Crossrefs

Decimal version of A065447.

Cf. A065761.

Programs

Maple

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

Mathematica

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 *)

PARI

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

Formula

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