

A099811


a(n) = a(n1) XOR Sum_{k=1..n1} a(k), with a(1)=1, a(2)=3, where XOR is the binary exclusive OR operation.


1



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,
1,1,1,
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(n1), sum(k=1, n1, 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



