A367307 Reverse bits in blocks in binary expansion of n where blocks are separated by every second 1 bit starting from the most significant 1 bit as the first separator.

0, 1, 2, 3, 4, 6, 5, 7, 8, 12, 10, 13, 9, 11, 14, 15, 16, 24, 20, 25, 18, 21, 26, 27, 17, 19, 22, 23, 28, 30, 29, 31, 32, 48, 40, 49, 36, 41, 50, 51, 34, 37, 42, 43, 52, 54, 53, 55, 33, 35, 38, 39, 44, 46, 45, 47, 56, 60, 58, 61, 57, 59, 62, 63, 64, 96, 80, 97

Offset

0,3

Comments

Self-inverse permutation of nonnegative integers.

Links

Rémy Sigrist, Table of n, a(n) for n = 0..8192

Index entries for sequences that are permutations of the nonnegative integers

Formula

a(n) = b(c(f(n)) + g(n)) = b(h(c(n))) for n > 0 with a(0) = 0 where

b(n) = b(f(h(n))) + g(n) for n > 0 with b(0) = 0,

c(n) = h(c(f(n)) + g(n)) for n > 0 with c(0) = 0,

f(n) = A053645(n), g(n) = A053644(n) and where h(n) = A059893(n).

Note that c (A333776) is the inverse permutation to b (A333777).

a(n) < 2^k iff n < 2^k for k >= 0.

Example

For n = 100930, reversals are each (...) block
  n    = 100930 = binary 1(1000)1(0100)1(000010)
  a(n) = 72016  = binary 1(0001)1(0010)1(010000)

Prog

(PARI) a(n) = my(v1); v1 = binary(n); my(A = 1); while(A <= #v1, my(B = A, C = 0, D); A++; while(A <= #v1, C += v1[A]; if(v1[A] && (C == 1), D = A); if(C < 2, A++, break)); if(C > 0, v1[D] = 0; v1[A + B - D] = 1)); fromdigits(v1, 2)

Crossrefs

Cf. A053644, A053645, A059893, A333776, A333777.

Sequence in context: A104464 A352725 A372128 * A139706 A333777 A306869

Adjacent sequences: A367304 A367305 A367306 * A367308 A367309 A367310

Keyword

nonn,base,easy

Author

Mikhail Kurkov, Nov 13 2023

Status

approved