A280510 -id:A280510 - cp's OEIS frontend

A280512 Index sequence of the Thue-Morse sequence (A010060, using offset 1) as a reverse block-fractal sequence.

1, 3, 2, 1, 12, 11, 10, 9, 8, 7, 6, 5, 4, 3, 2, 1, 48, 47, 46, 45, 44, 43, 42, 41, 40, 39, 38, 37, 36, 35, 34, 33, 32, 31, 30, 29, 28, 27, 26, 25, 24, 23, 22, 21, 20, 19, 18, 17, 16, 15, 14, 13, 12, 11, 10, 9, 8, 7, 6, 5, 4, 3, 2, 1, 192, 191, 190, 189, 188

Offset: 1

Clark Kimberling, Feb 10 2017

See A280511 for definitions. Note that the records, 3,12,48,192,... are also records in A280510, if A010060 is indexed with offset 1 instead of 0; see Example.

			A010060 = (0,1,1,0,1,0,0,1,1,0,0,1,0,1,1,0,1,0,0,1,0,,...) = (s(1), s(2), ... ).
(init. bl. #1) = (0); reversal = (0), first occurs s(1), so that a(1) = 1;
(init. bl. #2) = (0,1); reversal = (1,0) first occurs at s(3), so that a(2) = 3;
(init. bl. #3) = (0,1,1); reversal = (1,1,0) first occurs s(2), so that a(3) = 2.

Cf. A010060, A280510, A280511, A280513.

seq = Table[Mod[Length[FixedPointList[BitAnd[#, # - 1] &, n]], 2], {n, 0, 400}]  (* A010060 *)
seq = StringJoin[Map[ToString, seq]]
breverse[seq_] := Flatten[Last[Reap[NestWhile[# + 1 &, 1, (StringLength[
str = StringTake[seq, Min[StringLength[seq], #]]] == # && ! (Sow[
StringPosition[seq, StringReverse[str], 1][[1]][[1]]]) === {}) &]]]];
breverse[seq] (* A280512 *) (* Peter J. C. Moses, Jan 01 2017 *)

A337909 Distinct terms of A080079 in the order in which they appear.

Original entry on oeis.org

1, 2, 4, 3, 8, 7, 6, 5, 16, 15, 14, 13, 12, 11, 10, 9, 32, 31, 30, 29, 28, 27, 26, 25, 24, 23, 22, 21, 20, 19, 18, 17, 64, 63, 62, 61, 60, 59, 58, 57, 56, 55, 54, 53, 52, 51, 50, 49, 48, 47, 46, 45, 44, 43, 42, 41, 40, 39, 38, 37, 36, 35, 34, 33, 128

Offset: 1

Lorenzo Sauras Altuzarra, Sep 29 2020

nonn

This sequence is a permutation of the positive integers.

The cardinality of {2^k, ..., (2^k - 0^k)/2 + 1} is A011782(k).

			(2^0, ..., (2^0 - 0^0)/2 + 1) = (1),
(2^1, ..., (2^1 - 0^1)/2 + 1) = (2),
(2^2, ..., (2^2 - 0^2)/2 + 1) = (4, 3),
(2^3, ..., (2^3 - 0^3)/2 + 1) = (8, 7, 6, 5)...

Index entries for sequences that are permutations of the natural numbers

Cf. A004761, A011782, A053644, A054429, A080079, A280510.

{1}~Join~Array[3*2^(IntegerLength[# - 1, 2] - 1) - # + 1 &, 64, 2] (* Michael De Vlieger, Oct 05 2020 *)

a(n) = if(n--, 3<Kevin Ryde, Sep 29 2020

a(1) = 1 and a(n) = A080079(n - 1 + 2^floor(log_2(n - 1))) if n > 1.
a(n) = A080079(A004761(n+1)).
From Kevin Ryde, Sep 29 2020: (Start)
a(n) = 3*A053644(n-1) - (n-1), if n > 1.
a(n) = A054429(n-1) + 1, if n > 1.
a(n) = A280510(n) - n + 1, if n > 1. (End)

cp's OEIS Frontend

A280512 Index sequence of the Thue-Morse sequence (A010060, using offset 1) as a reverse block-fractal sequence.

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