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 A092569 Permutation of integers a(a(n)) = n. In binary representation of n, transformation of inner bits, 1 <-> 0, gives binary representation of a(n). 12
 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 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,3 COMMENTS Primes which stay primes under transformation "opposite inner bits", A092570. This permutation transforms the enumeration system of positive irreducible fractions A020651/A020650 into the enumeration system A245327/A245326, and vice versa. - Yosu Yurramendi, Jun 16 2015 A117120(a(n)) = a(A117120(n)), n > 0. A258996(a(n)) = a(A258996(n)), n > 0. A258746(a(n)) = a(A258746(n)), n > 0. A054429(a(n)) = a(A054429(n)), n > 0. a(n) = A054429(A065190(n)) = A065190(A054429(n), n > 0. - Yosu Yurramendi, Mar 23 2017 LINKS Michael De Vlieger, Table of n, a(n) for n = 0..10000 FORMULA 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 EXAMPLE a(9)=15 because 9_10 = 1001_2, transformation of inner bits gives 1001_2 -> 1111_2 = 15_10. MATHEMATICA 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 *) PROG (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)}; for(n=0, 70, print1(T(n), ", ")) \\ Washington Bomfim, Jan 18 2011 (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 # Yosu Yurramendi, Apr 10 2017 CROSSREFS Cf. A092570. Sequence in context: A368160 A234613 A258996 * A361996 A191726 A234025 Adjacent sequences: A092566 A092567 A092568 * A092570 A092571 A092572 KEYWORD nonn,base,easy AUTHOR Zak Seidov, Feb 28 2004 STATUS approved

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Last modified August 9 05:47 EDT 2024. Contains 375027 sequences. (Running on oeis4.)