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A038713
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a(n) = n XOR (n-1), i.e. nim-sum of sequential pairs, written in binary.
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1
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1, 11, 1, 111, 1, 11, 1, 1111, 1, 11, 1, 111, 1, 11, 1, 11111, 1, 11, 1, 111, 1, 11, 1, 1111, 1, 11, 1, 111, 1, 11, 1, 111111, 1, 11, 1, 111, 1, 11, 1, 1111, 1, 11, 1, 111, 1, 11, 1, 11111, 1, 11, 1, 111, 1, 11, 1, 1111, 1, 11, 1, 111, 1, 11, 1, 1111111, 1, 11, 1, 111, 1
(list; graph; refs; listen; history; internal format)
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OFFSET
| 1,2
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LINKS
| Index entries for sequences related to Nim-sums
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FORMULA
| a(n) = (10^A001511(n)-1)/(10-1)
Multiplicative with a(2^e)=(10^(e+1)-1)/9, a(p^e)=1 if p odd.
Multiplicative with a(p^e) = (10^e-1)/9 if p = 2, 1 otherwise
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EXAMPLE
| a(6) = 11 because 110 XOR 101 = 11 base 2
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PROG
| (PARI) a(n)=if(n<1, 0, (10^(valuation(n, 2)+1)-1)/9) /* Michael Somos Apr 28 2005 */
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CROSSREFS
| Cf. A038712 translated to binary, A001511 translated to unary (repeated 1's)
Sequence in context: A086994 A104490 A164851 * A130556 A120449 A101623
Adjacent sequences: A038710 A038711 A038712 * A038714 A038715 A038716
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KEYWORD
| mult,easy,nonn
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AUTHOR
| Henry Bottomley (se16(AT)btinternet.com), May 02 2000
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