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 A099895 XOR BINOMIAL transform of A000069 (Odious numbers). 1
 1, 3, 5, 0, 9, 0, 0, 0, 17, 0, 0, 0, 0, 0, 0, 0, 33, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 65, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 129 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,2 COMMENTS See A099884 for the definitions of the XOR BINOMIAL transform and the XOR difference triangle. LINKS FORMULA a(2^n) = 2^(n+1)+1 for n>0, with a(0)=1 and a(k)=0 otherwise. a(n) = SumXOR_{i=0..n} (C(n, i)mod 2)*A000069(n-i) and SumXOR is summation under XOR. EXAMPLE XOR difference triangle of A000069 begins: [1], [2,3], [4,6,5], [7,3,5,0], [8,15,12,9,9], [11,3,12,0,9,0], [13,6,5,9,9,0,0], [14,3,5,0,9,0,0,0], [16,30,29,24,24,17,17,17,17],... where A000069 is in the left-most column, and this sequence forms the main diagonal. PROG (PARI) {a(n)=local(B); B=0; for(i=0, n, B=bitxor(B, binomial(n, i)%2*A000069(n-i) )); B} CROSSREFS Cf. A099884, A000069, A099896. Sequence in context: A222480 A021289 A200480 * A124222 A200615 A111823 Adjacent sequences:  A099892 A099893 A099894 * A099896 A099897 A099898 KEYWORD nonn AUTHOR Paul D. Hanna, Oct 29 2004 STATUS approved

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Last modified May 21 21:50 EDT 2013. Contains 225505 sequences.