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

1,2

Links

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

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

Example

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

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 *)

Prog

(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

Crossrefs

Decimal version of A065447.

Cf. A065761.

Sequence in context: A361544 A178920 A066399 * A132612 A129463 A299426

Adjacent sequences: A065757 A065758 A065759 * A065761 A065762 A065763

Keyword

base,easy,nonn

Author

Lior Manor, Nov 18 2001

Status

approved