%I #11 Apr 20 2020 09:30:50
%S 2,3,5,7,11,13,23,27,45,55,91,109,183,219,365,439,731,877,1463,1755,
%T 2925,3511,5851,7021,11703,14043,23405,28087,46811,56173,93623,112347,
%U 187245,224695,374491,449389,748983,898779,1497965,1797559,2995931,3595117,5991863
%N (a(n-2) XOR a(n-1)) OR (highest bit of a(n-2))*2 OR 1; a(0)=2, a(1)=3.
%H Wikipedia, <a href="https://en.wikipedia.org/wiki/Bitwise operation">Bitwise operation</a>
%H <a href="/index/Bi#binary">Index entries for sequences related to binary expansion of n</a>
%e 5 = 101 = (1<<len( 10)) or ( 10 xor 11) or 1 = 100 | 1 | 1
%e 7 = 111 = (1<<len( 11)) or ( 11 xor 101) or 1 = 100 | 110 | 1
%e 11 = 1011 = (1<<len( 101)) or ( 101 xor 111) or 1 = 1000 | 10 | 1
%e 13 = 1101 = (1<<len( 111)) or ( 111 xor 1011) or 1 = 1000 | 1100 | 1
%e 23 = 10111 = (1<<len( 1011)) or ( 1011 xor 1101) or 1 = 10000 | 110 | 1
%e 27 = 11011 = (1<<len( 1101)) or ( 1101 xor 10111) or 1 = 10000 | 11010 | 1
%e 45 = 101101 = (1<<len(10111)) or (10111 xor 11011) or 1 = 100000 | 1100 | 1
%p a:= proc(n) option remember; uses Bits; `if`(n<2, n+2,
%p Or(1, Or(2^ilog2(2*a(n-2)), Xor(a(n-2), a(n-1)))))
%p end:
%p seq(a(n), n=0..50); # _Alois P. Heinz_, Apr 13 2020
%o (Ruby) v=[2,3];100.times{a=v[-2];b=v[-1];v<<((1<<a.bit_length)|(a^b)|1)};p v
%o (PARI) f(x,y)=bitor(1<<(exponent(x)+1)+1, bitxor(x,y))
%o first(n)=if(n<1, return([2])); my(v=vector(n+1)); v[1]=2; v[2]=3; for(i=3,n+1, v[i]=f(v[i-2],v[i-1])); v \\ _Charles R Greathouse IV_, Apr 19 2020
%K nonn,base
%O 0,1
%A _Simon Strandgaard_, Apr 13 2020