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A321226
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Describe the binary representation of n in binary and convert back to decimal.
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2
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2, 3, 14, 5, 28, 59, 22, 7, 30, 115, 238, 117, 44, 91, 30, 9, 56, 123, 462, 229, 476, 955, 470, 119, 46, 179, 366, 181, 60, 123, 38, 11, 58, 227, 494, 245, 924, 1851, 918, 231, 478, 1907, 3822, 1909, 940, 1883, 478, 233, 88, 187, 718, 357, 732, 1467, 726, 183
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OFFSET
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0,1
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COMMENTS
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This sequence is a binary variant of the "Look and Say" sequence A045918.
There is only one fixed point: a(7) = 7.
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LINKS
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FORMULA
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a(2^n - 1) = 2*n + 1 for any n > 0.
a(4*n + 1) = 4*a(2*n) + 3 for any n > 0.
a(4*n + 2) = 4*a(2*n + 1) + 2 for any n >= 0.
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EXAMPLE
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For n = 67:
- the binary representation of 67 is "1000011",
- we see, in binary: "1" "1", "100" "0", "10" "1",
- hence the binary representation of a(67) is "111000101",
- and a(67) = 453 in decimal.
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PROG
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(PARI) a(n, b=2) = if (n==0, return (b)); my (d=digits(b*n, b), v=0, w=0); d[#d] = -1; for (i=1, #d-1, w++; if (d[i]!=d[i+1], v = b*(v*b^#digits(w, b) + w) + d[i]; w = 0)); v
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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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