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A162951
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a(1)=0. a(n) is the smallest integer > a(n-1) such that both a(n) and a(n)-a(n-1) have the same number of 1's when written in binary as n has when it is written in binary.
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0
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OFFSET
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1,3
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COMMENTS
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a(7)=41 is the final term because 8 has one binary 1, which means that a(8), if it existed, must be a power of 2, and a(8)-41 must be a power of 2. Since no two powers of 2 have a difference of 41, then the sequence has only 7 terms.
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LINKS
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MATHEMATICA
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nxt[{n_, a_}]:=Module[{k=a+1}, While[DigitCount[n+1, 2, 1] != DigitCount[k, 2, 1] || DigitCount[k, 2, 1] != DigitCount[k-a, 2, 1], k++]; {n+1, k}]; Transpose[ NestList[nxt, {1, 0}, 6]][[2]] (* Harvey P. Dale, Dec 07 2012 *)
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CROSSREFS
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KEYWORD
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fini,full,nonn
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AUTHOR
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STATUS
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approved
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