A115873 First column of A115872.

1, 1, 3, 1, 7, 3, 7, 1, 15, 7, 3, 3, 5, 7, 15, 1, 31, 15, 7, 7, 31, 3, 7, 3, 31, 5, 31, 7, 31, 15, 31, 1, 63, 31, 15, 15, 7, 7, 7, 7, 63, 31, 3, 3, 63, 7, 15, 3, 21, 31, 63, 5, 63, 31, 7, 7, 9, 31, 63, 15, 21, 31, 63, 1, 127, 63, 31, 31, 15, 15, 15, 15, 127, 7, 31, 7, 15, 7, 15, 7, 51

Offset

1,3

Links

Table of n, a(n) for n=1..81.

Formula

a(2^k) = 1, a(2n) = a(n).

Mathematica

X[a_, b_] := Module[{A, B, C, x},
   A = Reverse@IntegerDigits[a, 2];
   B = Reverse@IntegerDigits[b, 2];
   C = Expand[
      Sum[A[[i]]*x^(i - 1), {i, 1, Length[A]}]*
      Sum[B[[i]]*x^(i - 1), {i, 1, Length[B]}]];
   PolynomialMod[C, 2] /. x -> 2];
T[n_, k_] := Module[{x = BitXor[n - 1, 2 n - 1], k0 = k},
     For[i = 1, True, i++, If[n*i == X[x, i],
     If[k0 == 1, Return[i], k0--]]]];
a[n_] := T[n, 1];
Table[a[n], {n, 1, 100}] (* Jean-François Alcover, Jan 04 2022 *)

Crossrefs

Cf. A114395, A114396, A115872.

Sequence in context: A053092 A212045 A292849 * A329369 A083239 A333847

Adjacent sequences: A115870 A115871 A115872 * A115874 A115875 A115876

Keyword

nonn

Author

Antti Karttunen, Feb 07 2006

Status

approved