cp's OEIS Frontend

A381406 a(0) = 0; for n > 0, a(n) is the smallest unused number such that a(n) OR a(n-1) = 2^k - 1, where OR is the binary OR operation and k>=1, while the binary weight of a(n) does not equal that of a(n-1).

%I A381406 #8 Feb 23 2025 09:31:44
%S A381406 0,1,3,2,5,7,4,11,6,13,10,15,8,23,9,14,17,30,19,12,27,20,31,16,47,18,
%T A381406 29,22,43,21,46,25,39,24,55,26,45,50,61,34,63,28,51,44,59,36,91,37,58,
%U A381406 69,62,33,94,35,60,67,124,71,56,79,48,95,32,127,38,57,70,121,54,41,86,107,52,75,117,42,53,74,119,40,87,104,151,105,118,73,126,49,78,115
%N A381406 a(0) = 0; for n > 0, a(n) is the smallest unused number such that a(n) OR a(n-1) = 2^k - 1, where OR is the binary OR operation and k>=1, while the binary weight of a(n) does not equal that of a(n-1).
%C A381406 The fixed points begin 0, 1, 10, 315, 413, 415, 1551, 1559, 1797; there are likely infinitely more.
%H A381406 Scott R. Shannon, <a href="/A381406/b381406.txt">Table of n, a(n) for n = 0..10000</a>
%e A381406 a(4) = 5 = 101_2 as 5 is unused and a(3) = 2 = 10_2, and 101_2 OR 10_2 = 111_2 = 2^3 - 1, while the binary weights of 5 and 2 are 2 and 1 respectively.
%Y A381406 Cf. A000120, A086799, A061712, A057168, A381405.
%K A381406 nonn,base
%O A381406 0,3
%A A381406 _Scott R. Shannon_, Feb 22 2025