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A100922
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n appears A000120(n) times (appearances equal number of 1-bits).
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4
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1, 2, 3, 3, 4, 5, 5, 6, 6, 7, 7, 7, 8, 9, 9, 10, 10, 11, 11, 11, 12, 12, 13, 13, 13, 14, 14, 14, 15, 15, 15, 15, 16, 17, 17, 18, 18, 19, 19, 19, 20, 20, 21, 21, 21, 22, 22, 22, 23, 23, 23, 23, 24, 24, 25, 25, 25, 26, 26, 26, 27, 27, 27, 27, 28, 28, 28, 29, 29, 29, 29, 30, 30, 30
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listen;
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OFFSET
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0,2
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COMMENTS
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Clearly every positive integer appears at least once in this sequence.
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LINKS
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FORMULA
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Sum_{n>=1} (-1)^(n+1)/a(n) = Sum_{n>=1} (-1)^(n+1)/A000069(n) = 0.67968268... . - Amiram Eldar, Feb 18 2024
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EXAMPLE
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The binary representation of 16 is 10000, which has one 1-bit (and four 0-bits), hence 16 appears once in this sequence (and four times in A100921).
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MATHEMATICA
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Table[Table[n, DigitCount[n, 2, 1]], {n, 30}]//Flatten (* Harvey P. Dale, Aug 31 2017 *)
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PROG
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CROSSREFS
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KEYWORD
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base,easy,nonn
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AUTHOR
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STATUS
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approved
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