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

Author

Antti Karttunen, Feb 07 2006

Keywords

• nonn

Crossrefs

Cf. A114395, A114396, A115872.

Programs

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 *)

Formula

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