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Search: id:A115379
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| A115379 |
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Number of positive integers k < n such that n XOR k < n and GCD(n,k) is odd. |
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+0
1
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| 0, 1, 0, 3, 0, 3, 2, 7, 0, 3, 2, 7, 4, 11, 6, 15, 0, 3, 2, 7, 4, 11, 6, 15, 8, 19, 10, 23, 12, 27, 14, 31, 0, 3, 2, 7, 4, 11, 6, 15, 8, 19, 10, 23, 12, 27, 14, 31, 16, 35, 18, 39, 20, 43, 22, 47, 24, 51, 26, 55, 28, 59, 30, 63, 0, 3, 2, 7, 4, 11, 6, 15, 8, 19, 10, 23, 12, 27, 14, 31, 16, 35
(list; graph; listen)
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OFFSET
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0,4
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COMMENT
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A059029 equals the limiting sequence of 2^k consecutive terms of this sequence starting at position 2^k as k increases, where A059029(n) = n if n is even, 2n+1 if n is odd.
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FORMULA
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a(2^n) = 0, a(2^n-1) = 2^n-1, for n>=0. a(2^n+1)=3 (n>0), a(2^n+2)=2 (n>1)), a(2^n+3)=7 (n>1), a(2^n+4)=4 (n>2), a(2^n+5)=11 (n>2), etc.
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PROGRAM
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(PARI) a(n)=sum(k=0, n, if(bitxor(n, k)<n&gcd(n, k)%2==1, 1, 0))
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CROSSREFS
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Cf. A059029, A006257 (Josephus problem).
Adjacent sequences: A115376 A115377 A115378 this_sequence A115380 A115381 A115382
Sequence in context: A004604 A016035 A112470 this_sequence A127801 A096597 A097994
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KEYWORD
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nonn
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AUTHOR
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Paul D. Hanna (pauldhanna(AT)juno.com), Jan 21 2006
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