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A092569
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Permutation of integers a(a(n)) = n. In binary representation of n, transformation of inner bits, 1 <-> 0, gives binary representation of a(n).
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12
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0, 1, 2, 3, 6, 7, 4, 5, 14, 15, 12, 13, 10, 11, 8, 9, 30, 31, 28, 29, 26, 27, 24, 25, 22, 23, 20, 21, 18, 19, 16, 17, 62, 63, 60, 61, 58, 59, 56, 57, 54, 55, 52, 53, 50, 51, 48, 49, 46, 47, 44, 45, 42, 43, 40, 41, 38, 39, 36, 37, 34, 35, 32, 33, 126, 127, 124, 125, 122, 123, 120
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OFFSET
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0,3
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COMMENTS
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Primes which stay primes under transformation "opposite inner bits", A092570.
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LINKS
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FORMULA
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a(0) = 0, a(1) = 1, a(2) = 2, a(3) = 3, a(2^(m+1) +k) = a(2^m+k) + 2^(m+1),
a(2^(m+1)+2^m+k) = a(2^m+k) + 2^m, m >= 1, 0 <= k < 2^m. - Yosu Yurramendi, Apr 02 2017
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EXAMPLE
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a(9)=15 because 9_10 = 1001_2, transformation of inner bits gives 1001_2 -> 1111_2 = 15_10.
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MATHEMATICA
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bb={0, 1, 2, 3}; Do[id=IntegerDigits[n, 2]; Do[id[[i]]=1-id[[i]], {i, 2, Length[id]-1}]; bb=Append[bb, FromDigits[id, 2]], {n, 4, 1000}]; fla=Flatten[bb]
(* Second program: *)
Table[If[n < 2, n, Function[b, FromDigits[#, 2] &@ Join[{First@ b}, Most[Rest@ b] /. { 0 -> 1, 1 -> 0}, {Last@ b}]]@ IntegerDigits[n, 2]], {n, 0, 70}] (* Michael De Vlieger, Apr 03 2017 *)
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PROG
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(PARI)T(n)={pow2=2; v=binary(n); L=#v-1; forstep(k=L, 2, -1, if(v[k], n-=pow2, n+=pow2); pow2*=2); return(n)};
(R)
maxrow <- 8 # by choice
a <- 1:3 # If it were c(1, 3, 2), it would be A054429
for(m in 1:maxrow) for(k in 0:(2^m-1)){
a[2^(m+1)+ k] = a[2^m+k] + 2^(m+1)
a[2^(m+1)+2^m+k] = a[2^m+k] + 2^m
}
a
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CROSSREFS
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KEYWORD
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nonn,base,easy
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AUTHOR
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STATUS
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approved
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