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A352458
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2^k appears in the binary expansion of a(n) iff 2^k appears in the binary expansion of n and k AND n = 0 (where AND denotes the bitwise AND operator).
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5
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0, 1, 2, 1, 4, 5, 2, 1, 8, 1, 2, 1, 12, 5, 2, 1, 16, 17, 18, 17, 4, 5, 2, 1, 24, 17, 18, 17, 12, 5, 2, 1, 32, 1, 34, 1, 4, 5, 2, 1, 40, 1, 34, 1, 12, 5, 2, 1, 48, 17, 50, 17, 4, 5, 2, 1, 56, 17, 50, 17, 12, 5, 2, 1, 64, 65, 2, 1, 4, 5, 2, 1, 72, 65, 2, 1, 12
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OFFSET
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0,3
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COMMENTS
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The idea is to keep the 1's in the binary expansion of a number whose positions are related in some way to that number.
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LINKS
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Rémy Sigrist, Table of n, a(n) for n = 0..8192
Index entries for sequences related to binary expansion of n
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FORMULA
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a(n) <= n with equality iff n belongs to A335702.
a(n) = n - A309274(n).
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EXAMPLE
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For n = 42:
- 42 = 2^5 + 2^3 + 2^1,
- 42 AND 5 = 0,
- 42 AND 3 = 2 <> 0,
- 42 AND 1 = 0,
- so a(42) = 2^5 + 2^1 = 34.
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PROG
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(PARI) a(n) = { my (v=0, m=n, k); while (m, m-=2^k=valuation(m, 2); if (bitand(n, k)==0, v+=2^k)); v }
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CROSSREFS
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See A352449, A352450, A352451, A352452 for similar sequences.
Cf. A335702 (fixed points).
Sequence in context: A114158 A248666 A162407 * A132741 A072436 A247503
Adjacent sequences: A352455 A352456 A352457 * A352459 A352460 A352461
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KEYWORD
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nonn,base
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AUTHOR
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Rémy Sigrist, Mar 17 2022
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STATUS
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approved
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