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A145849 a(n) = A145812(2n-1). 3
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 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,2

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

FORMULA

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

MATHEMATICA

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

PROG

(PARI) a145812(n) = 2*fromdigits(binary(n-1), 4) + 1;

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

CROSSREFS

Bisection of A145812.

Sequence in context: A130444 A177697 A287534 * A111045 A020226 A175440

Adjacent sequences:  A145846 A145847 A145848 * A145850 A145851 A145852

KEYWORD

nonn

AUTHOR

Vladimir Shevelev, Oct 21 2008

EXTENSIONS

More terms from Michel Marcus, Dec 13 2018

STATUS

approved

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Last modified January 16 15:53 EST 2019. Contains 319195 sequences. (Running on oeis4.)