A145849 a(n) = A145812(2n-1).

1, 9, 33, 41, 129, 137, 161, 169, 513, 521, 545, 553, 641, 649, 673, 681, 2049, 2057, 2081, 2089, 2177, 2185, 2209, 2217, 2561, 2569, 2593, 2601, 2689, 2697, 2721, 2729, 8193, 8201, 8225, 8233, 8321, 8329, 8353, 8361, 8705, 8713, 8737, 8745, 8833, 8841, 8865, 8873, 10241

Offset: 1

Author

Vladimir Shevelev, Oct 21 2008

Keywords

• nonn

Comments

Every positive odd integer m==3 (mod 8) is a unique sum of the form a(s)+2a(t), while other odd integers are not expressible in this form.

Links

• Vincenzo Librandi, Table of n, a(n) for n = 1..5000

Crossrefs

Bisection of A145812.

Programs

Mathematica

a[n_] := 2 * FromDigits[IntegerDigits[2*n-2, 2], 4] + 1; Array[a, 50] (* Amiram Eldar, Dec 16 2018 *)

PARI

a145812(n) = 2*fromdigits(binary(n-1), 4) + 1;
a(n) = a145812(2*n-1); \\ Michel Marcus, Dec 13 2018

Formula

If f(x) = Sum_{n>=1}x^a(n), abs(x) < 1, then f(x)*f(x^2) = x^3/(1 - x^8).

Extensions

More terms from Michel Marcus, Dec 13 2018