cp's OEIS Frontend

A354780 a(n) is the bitwise OR of (the binary expansions of) b(n+1) to b(2*n), where b is A354169.

%I A354780 #26 Jul 08 2022 18:05:22
%S A354780 2,12,27,115,252,1004,2013,4031,16307,32631,65279,261375,524270,
%T A354780 2096110,4194253,8386527,16773119,67096575,134217659,536854459,
%U A354780 1073741623,2147450751,4294901759,17179672575,34359737599,137438690559,274877382143,549754765311,2199022205950,4398044412927,8796093022189,35184367894509,70368744175567
%N A354780 a(n) is the bitwise OR of (the binary expansions of) b(n+1) to b(2*n), where b is A354169.
%C A354780 If the binary expansion of a(n) has a 1 in the 2^i's bit (for any i >= 0) then A354169(2*n+1) must have a 0 in that bit.
%C A354780 A354169(2*n+1) is the smallest number not yet in A354169 which satisfies that condition (this follows at once from the definition of A354169).
%C A354780 This sequence bears the same relation to A354169 as A355057 does to A090252.
%H A354780 N. J. A. Sloane, <a href="/A354780/b354780.txt">Table of n, a(n) for n = 1..256</a>
%e A354780 Consider n=6. Then b(7) to b(12) are 32, 64, 12, 128, 256, 512. The bitwise OR of those 6 numbers is 1111101100_2 = 1004_10 = a(6). The bitwise complement of 1004_10 is 10011_2 = 19_10 = A354781(6), and A354169(6) = 17_10 = 10001_2.
%e A354780 On the other hand, for n=5, b(6) to b(10) are 16, 32, 64, 12, 128, whose bitwise OR is 11111100_2 = 252_10 = a(5). The bitwise complement of 252_10 is 3_10 = 11_2 = A354781(5). However, 3 has already appeared in A354169, and the smallest available number whose binary expansion is disjoint from 252_10 = 11111100_2 is 2^8 = 100000000_2 = 256_10 = 2^8 = A354169(5).
%Y A354780 A bisection of A354757.
%Y A354780 Cf. A354169, A354680, A354757, A354758, A354767, A354773, A354774, A354778, A355150, A354781.
%Y A354780 See also A090252, A355057.
%K A354780 nonn,base
%O A354780 1,1
%A A354780 _N. J. A. Sloane_, Jul 05 2022