A099811 - OEIS

A099811

a(n) = a(n-1) XOR Sum_{k=1..n-1} a(k), with a(1)=1, a(2)=3, where XOR is the binary exclusive OR operation.

1, 3, 7, 12, 27, 41, 114, 191, 307, 908, 1479, 2517, 7218, 11819, 20079, 57564, 94035, 233905, 327970, 954519, 1356507, 3827708, 5462751, 15712989, 21207042, 61631203, 87045927, 251438028, 339057531, 986402633, 1392602162, 4023051167

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OFFSET

1,2

LINKS

Table of n, a(n) for n=1..32.

EXAMPLE

a(3) = 7 since 3 XOR (3+1) = 3 XOR 4 = 7.

a(4) = 12 since 7 XOR (7+3+1) = 7 XOR 11 = 12.

a(5) = 27 since 12 XOR (12+7+3+1) = 12 XOR 23 = 27.

The binary expansions of a(n) form a triangle (listed with ones place in leftmost column):

1,1,

1,1,1,

0,0,1,1,

1,1,0,1,1,

1,0,0,1,0,1,

0,1,0,0,1,1,1,

1,1,1,1,1,1,0,1,

1,1,0,0,1,1,0,0,1,

0,0,1,1,0,0,0,1,1,1,

1,1,1,0,0,0,1,1,1,0,1,

1,0,1,0,1,0,1,1,1,0,0,1,...

PROG

(PARI) a(n)=if(n==1, 1, if(n==2, 3, bitxor(a(n-1), sum(k=1, n-1, a(k)))))

CROSSREFS

Cf. A099810.

Sequence in context: A062325 A301982 A196858 * A196917 A256259 A182941

Adjacent sequences: A099808 A099809 A099810 * A099812 A099813 A099814

KEYWORD

nonn

AUTHOR

Paul D. Hanna, Oct 26 2004

STATUS

approved