0,5

Also bitwise XOR of n with the nearest Mersenne number (A000225) larger than or equal to n, for n > 0. (For n = 0, a(0) = -1 as opposed to 1). The advantage of using BitXor instead of BaseForm in the Mathematica program is that the result has a Head of Integer, not BaseForm. - Alonso Delarte (alonso.delarte(AT)gmail.com), Jan 14 2006

J.-P. Allouche and J. Shallit, The ring of k-regular sequences, II, Theoret. Computer Sci., 307 (2003), 3-29.

J.-P. Allouche and J. Shallit, The Ring of k-regular Sequences, II

R. Stephan, Divide-and-conquer generating functions. I. Elementary sequences

R. Stephan, Some divide-and-conquer sequences ...

R. Stephan, Table of generating functions

a(n) = 2^k - n - 1, where 2^(k-1) < n < 2^k.

a(n+1) = (a(n)+n) mod (n+1); a(0) = 1. - Reinhard Zumkeller (reinhard.zumkeller(AT)gmail.com), Jul 22 2002

G.f.: 1 + 1/(1-x)*sum(k>=0, 2^k*x^2^(k+1)/(1+x^2^k)). - Ralf Stephan, May 06 2003

a(0) = 0, a(2n+1) = 2*a(n), a(2n) = 2*a(n) + 1 . - DELEHAM Philippe (kolotoko(AT)wanadoo.fr), Feb 29 2004

a(n) = number of positive integers k < n such that n XOR k > n. a(n) = n - A006257(n). - Paul D. Hanna (pauldhanna(AT)juno.com), Jan 21 2006

8 = 1000 -> 0111 = 111 = 7

Table[BaseForm[FromDigits[(IntegerDigits[i, 2]/.{0->1, 1->0}), 2], 10], {i, 0, 90}]

Table[BitXor[n, 2^IntegerPart[Log[2, n] + 1] - 1], {n, 100}] (Delarte)

(PARI) a(n)=sum(k=1, n, if(bitxor(n, k)>n, 1, 0)) (Hanna)

a(n) = A003817(n) - n, for n>0. Cf. A087734.

Cf. A000225, A006257 (Josephus problem).

Adjacent sequences: A035324 A035325 A035326 this_sequence A035328 A035329 A035330

Sequence in context: A051427 A098825 A111460 this_sequence A004444 A085771 A111106

nonn,easy,base

njas

More terms from Vit Planocka (planocka(AT)mistral.cz), Feb 01 2003

a(0) corrected by Paolo P. Lava (ppl(AT)spl.at), Oct 22 2007