cp's OEIS Frontend

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

%I A337909 #28 Oct 06 2020 02:34:42
%S A337909 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,
%T A337909 22,21,20,19,18,17,64,63,62,61,60,59,58,57,56,55,54,53,52,51,50,49,48,
%U A337909 47,46,45,44,43,42,41,40,39,38,37,36,35,34,33,128
%N A337909 Distinct terms of A080079 in the order in which they appear.
%C A337909 This sequence is a permutation of the positive integers.
%C A337909 The cardinality of {2^k, ..., (2^k - 0^k)/2 + 1} is A011782(k).
%H A337909 <a href="/index/Per#IntegerPermutation">Index entries for sequences that are permutations of the natural numbers</a>
%F A337909 a(1) = 1 and a(n) = A080079(n - 1 + 2^floor(log_2(n - 1))) if n > 1.
%F A337909 a(n) = A080079(A004761(n+1)).
%F A337909 From _Kevin Ryde_, Sep 29 2020: (Start)
%F A337909 a(n) = 3*A053644(n-1) - (n-1), if n > 1.
%F A337909 a(n) = A054429(n-1) + 1, if n > 1.
%F A337909 a(n) = A280510(n) - n + 1, if n > 1. (End)
%e A337909 (2^0, ..., (2^0 - 0^0)/2 + 1) = (1),
%e A337909 (2^1, ..., (2^1 - 0^1)/2 + 1) = (2),
%e A337909 (2^2, ..., (2^2 - 0^2)/2 + 1) = (4, 3),
%e A337909 (2^3, ..., (2^3 - 0^3)/2 + 1) = (8, 7, 6, 5)...
%t A337909 {1}~Join~Array[3*2^(IntegerLength[# - 1, 2] - 1) - # + 1 &, 64, 2] (* _Michael De Vlieger_, Oct 05 2020 *)
%o A337909 (PARI) a(n) = if(n--, 3<<logint(n,2) - n, 1); \\ _Kevin Ryde_, Sep 29 2020
%Y A337909 Cf. A004761, A011782, A053644, A054429, A080079, A280510.
%K A337909 nonn
%O A337909 1,2
%A A337909 _Lorenzo Sauras Altuzarra_, Sep 29 2020