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A338888 a(n) = (a(n-2) bitwise-OR a(n-1)) + 1; a(1)=0, a(2)=0.

%I A338888 #25 Aug 02 2023 14:08:20
%S A338888 0,0,1,2,4,7,8,16,25,26,28,31,32,64,97,98,100,103,104,112,121,122,124,
%T A338888 127,128,256,385,386,388,391,392,400,409,410,412,415,416,448,481,482,
%U A338888 484,487,488,496,505,506,508,511,512,1024,1537,1538,1540,1543,1544
%N A338888 a(n) = (a(n-2) bitwise-OR a(n-1)) + 1; a(1)=0, a(2)=0.
%H A338888 Harvey P. Dale, <a href="/A338888/b338888.txt">Table of n, a(n) for n = 1..1000</a>
%H A338888 Wikipedia, <a href="https://en.wikipedia.org/wiki/Bitwise operation">Bitwise operation</a>
%F A338888 a(6*2^n+k) = 8 * min(3,k) * 4^n + a(k), where k is positive and as small as possible. - _Charlie Neder_, Jul 31 2023
%e A338888 a(3) = (0 | 0) + 1 =  0 + 1 =  1,
%e A338888 a(4) = (0 | 1) + 1 =  1 + 1 =  2,
%e A338888 a(5) = (1 | 2) + 1 =  3 + 1 =  4,
%e A338888 a(6) = (2 | 4) + 1 =  6 + 1 =  7,
%e A338888 a(7) = (4 | 7) + 1 =  7 + 1 =  8,
%e A338888 a(8) = (7 | 8) + 1 = 15 + 1 = 16.
%t A338888 a[1] = a[2] = 0; a[n_] := a[n] = BitOr[a[n - 1], a[n - 2]] + 1; Array[a, 55] (* _Amiram Eldar_, Nov 14 2020 *)
%t A338888 nxt[{a_,b_}]:={b,BitOr[a,b]+1}; NestList[nxt,{0,0},60][[All,1]] (* _Harvey P. Dale_, May 08 2021 *)
%o A338888 (Ruby) values = [0, 0]
%o A338888 30.times { values << (values[-2] | values[-1]) + 1 }
%o A338888 p values
%o A338888 (PARI) lista(nn) = {my(va = vector(nn)); for (n=3, nn, va[n] = bitor(va[n-2], va[n-1]) + 1;); va;} \\ _Michel Marcus_, Nov 14 2020
%o A338888 (Python 3.8+) a338888 = lambda n: (0,0,1,2,4,7)[n-1] if n<7 else (8*4**(k:=((n-1)//6).bit_length()-1)*min(3,d:=n-6*2**k)+a338888(d)) # _Charlie Neder_, Jul 31 2023
%K A338888 nonn
%O A338888 1,4
%A A338888 _Simon Strandgaard_, Nov 14 2020