A125050 -id:A125050 - cp's OEIS frontend

A019299 First n elements of Thue-Morse sequence A010059 read as a binary number.

1, 2, 4, 9, 18, 37, 75, 150, 300, 601, 1203, 2406, 4813, 9626, 19252, 38505, 77010, 154021, 308043, 616086, 1232173, 2464346, 4928692, 9857385, 19714771, 39429542, 78859084, 157718169, 315436338, 630872677, 1261745355, 2523490710, 5046981420

Offset: 0

Jonas Wallgren

nonn

Cf. A001969 (evil numbers), A010060, A014571, A125050.

a:= n-> add((1+(-1)^irem(add(j, j=convert(n-i, base, 2)), 2))*2^i/2, i=0..n):
seq(a(n), n=0..32); # Lorenzo Sauras Altuzarra, Jan 31 2023

a(n) = Sum_{k=0..n} (1+(-1)^A010060(n-k))*2^k/2. - Paul Barry, Jan 06 2005
From Lorenzo Sauras Altuzarra, Jan 31 2023: (Start)
a(n+1) = 2*a(n) + 1 if a(n) is evil; a(n+1) = 2*a(n) otherwise (see also A125050).
a(n) = floor((1-c)*2^(n+1)), where c = A014571 is the Thue - Morse constant. (End)

A125049 a(1) = 1. If a(n) is prime, a(n+1) = 2a(n); otherwise, a(n+1) = 2a(n) + 1.

Original entry on oeis.org

1, 3, 6, 13, 26, 53, 106, 213, 427, 855, 1711, 3423, 6847, 13695, 27391, 54783, 109567, 219134, 438269, 876539, 1753079, 3506159, 7012318, 14024637, 28049275, 56098551, 112197103, 224394207, 448788415, 897576831, 1795153663, 3590307326

Offset: 1

Franklin T. Adams-Watters, Nov 17 2006

nonn

Cf. A125050.

a := proc(n)
   local c, k:
   c, k := 1, 1:
   while c < n do
      if isprime(k) then k := 2*k: else k := 2*k+1: fi:
      c := c+1: od:
   k: end: # Lorenzo Sauras Altuzarra, Jan 02 2023

NestList[If[PrimeQ[#],2#,2#+1]&,1,40] (* Harvey P. Dale, Sep 01 2017 *)

a(n) = floor(c*2^n), where c = 0.8359335658... - Lorenzo Sauras Altuzarra, Jan 01 2023

cp's OEIS Frontend

A019299 First n elements of Thue-Morse sequence A010059 read as a binary number.

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A125049 a(1) = 1. If a(n) is prime, a(n+1) = 2a(n); otherwise, a(n+1) = 2a(n) + 1.

Views

Author

Keywords

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Maple

Mathematica

Formula

cp's OEIS Frontend

A019299 First n elements of Thue-Morse sequence A010059 read as a binary number.

Views

Author

Keywords

Crossrefs

Programs

Maple

Formula

A125049 a(1) = 1. If a(n) is prime, a(n+1) = 2*a(n); otherwise, a(n+1) = 2*a(n) + 1.

Views

Author

Keywords

Crossrefs

Programs

Maple

Mathematica

Formula

A125049 a(1) = 1. If a(n) is prime, a(n+1) = 2a(n); otherwise, a(n+1) = 2a(n) + 1.