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A145342
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a(n) = (A145341(n) + 1)/2.
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3
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1, 2, 3, 4, 5, 7, 6, 8, 9, 13, 11, 15, 10, 14, 12, 16, 17, 25, 21, 29, 19, 27, 23, 31, 18, 26, 22, 30, 20, 28, 24, 32, 33, 49, 41, 57, 37, 53, 45, 61, 35, 51, 43, 59, 39, 55, 47, 63, 34, 50, 42, 58, 38, 54, 46, 62, 36, 52, 44, 60, 40, 56, 48, 64, 65, 97, 81, 113, 73, 105, 89
(list;
graph;
refs;
listen;
history;
text;
internal format)
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OFFSET
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1,2
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COMMENTS
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This sequence is a permutation of the positive integers. It is its own inverse permutation.
If the terms (n > 0) are written as an array (left-aligned fashion) with rows of length 2^m, m = 0,1,2,3,...
1;
2, 3;
4, 5, 7, 6;
8, 9, 13, 11, 15, 10, 14, 12;
16, 17, 25, 21, 29, 19, 27, 23, 31, 18, 26, 22, 30, 20, 28, 24;
32, 33, 49, 41, 57, 37, 53, 45, 61, 35, 51, 43, 59, 39, 55, 47, 63, 34, ...
then the following relationship can be observed:
a(1) = 1, a(2) = 2, a(3) = 3,
for m > 0, a(2^(m+1)) = 2*a(2^m), a(2^m + 1) = a(2^m) + 1, a(2^(m+1)+ 2^m) = 2*a(2^(m+1)) - 1, for 0 < k < 2^m, a(2^(m+1)+ k) = 2*a(2^m + k) - 1, a(2^(m+1)+ 2^m + k) = a(2^(m+1) + k) + 1
(End)
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LINKS
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MATHEMATICA
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Table[(FromDigits[Reverse[IntegerDigits[2n-1, 2]], 2] +1)/2, {n, 71}] (* Ivan Neretin, Oct 31 2015 *)
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PROG
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(R)
nmax <- 10^3 # by choice
b <- vector()
for (o in seq(1, nmax, 2)){
w <- which(as.numeric(intToBits(o))==1)
b <- c(b, sum(2^(max(w)-w)))
}
a <- (b+1)/2
a[1:71]
(PARI) a(n) = (1+fromdigits(Vecrev(binary(2*n-1)), 2))/2; \\ Michel Marcus, Feb 04 2019
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CROSSREFS
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KEYWORD
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base,nonn
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AUTHOR
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EXTENSIONS
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STATUS
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approved
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