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A322149
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In the binary representation of n, replace each run of k 0's (or 1's) with k^2 0's (or 1's).
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2
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0, 1, 2, 15, 16, 5, 30, 511, 512, 33, 10, 47, 240, 61, 1022, 65535, 65536, 1025, 66, 271, 80, 21, 94, 1535, 7680, 481, 122, 495, 8176, 2045, 131070, 33554431, 33554432, 131073, 2050, 8207, 528, 133, 542, 8703, 2560, 161, 42, 175, 752, 189, 3070, 196607, 983040
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OFFSET
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0,3
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COMMENTS
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This sequence has similarities with A001196: here we square the length of each run of consecutive equal bits, there we double it.
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LINKS
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FORMULA
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a(n) >= n with equality iff n belongs to A000975.
a(2^n) = 2^(n^2) for any n >= 0.
a(2^n - 1) = 2^(n^2) - 1 for any n >= 0.
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MATHEMATICA
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squareList[v_] := Flatten[ConstantArray[v, {Length[v]}]]; a[n_] := FromDigits[ Flatten[squareList /@ Split[IntegerDigits[n, 2]]], 2]; Array[a, 60, 0] (* Amiram Eldar, Dec 07 2018*)
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PROG
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(PARI) a(n) = if (n==0, 0, my (b=n%2, k=valuation(n+b, 2)); (a(n\2^k) + b) * 2^(k^2) - b)
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CROSSREFS
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KEYWORD
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nonn,base
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AUTHOR
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STATUS
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approved
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