

A344841


a(n) is the least positive number not of the form a(k) XOR ... XOR a(m) with 1 <= k <= m < n (where XOR denotes the bitwise XOR operator).


1



1, 2, 4, 5, 8, 12, 14, 16, 17, 19, 20, 21, 23, 32, 33, 35, 48, 49, 51, 56, 57, 59, 64, 65, 67, 68, 69, 71, 76, 77, 79, 80, 81, 83, 84, 85, 87, 92, 93, 95, 128, 129, 131, 132, 133, 135, 140, 141, 143, 192, 193, 195, 196, 197, 199, 204, 205, 207, 224, 225, 227
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OFFSET

1,2


COMMENTS

This sequence has similarities with A002048; here we use XOR, there addition.
All powers of 2 appear.


LINKS

Rémy Sigrist, Table of n, a(n) for n = 1..10000


FORMULA

Apparently, a(A246360(k)) = 2^(k1) for any k > 0.


EXAMPLE

n a(n) a(k) XOR ... XOR a(n) for k=1..n
  
1 1 1
2 2 3, 2
3 4 7, 6, 4
4 5 2, 3, 1, 5
5 8 10, 11, 9, 13, 8
6 12 6, 7, 5, 1, 4, 12
7 14 8, 9, 11, 15, 10, 2, 14
8 16 24, 25, 27, 31, 26, 18, 30, 16
9 17 9, 8, 10, 14, 11, 3, 15, 1, 17
10 19 26, 27, 25, 29, 24, 16, 28, 18, 2, 19


PROG

(PARI) s=2^0; for (n=1, #a=vector(61), print1 (a[n]=valuation(s+1, 2)", "); z=0; forstep (k=n, 1, 1, s=bitor(s, 2^z=bitxor(z, a[k]))))


CROSSREFS

Cf. A002048, A246360.
Sequence in context: A190190 A063465 A287346 * A035001 A260386 A092268
Adjacent sequences: A344838 A344839 A344840 * A344842 A344843 A344844


KEYWORD

nonn,base


AUTHOR

Rémy Sigrist, May 29 2021


STATUS

approved



