OFFSET
1,1
FORMULA
a(n) = floor(a(n-1)*3/2) bitwise-OR LSB(a(n-1)*n), with a(1)=2 (LSB = Least Significant Bit).
EXAMPLE
even index = x + (x>>1)
odd index = ((x + (x>>1)) | least significant bit of x
3 = 2 + 1
5 = (3 + 1) | 1
7 = 5 + 2
11 = (7 + 3) | 1
16 = 11 + 5
24 = (16 + 8) | 0
36 = 24 + 12
54 = (36 + 18) | 0
81 = 54 + 27
121 = (81 + 40) | 1
MATHEMATICA
a[1] = 2; a[n_] := a[n] = BitOr[Floor[a[n - 1]*3/2], Mod[a[n - 1]*n, 2]]; Array[a, 45] (* Amiram Eldar, May 01 2020 *)
PROG
(Ruby) values = [2]; 100.times { |index| x = values.last; values << ((x + (x>>1)) | (x&1&index)) }; p values
(PARI) lista(nn) = {my(a=2, va = List(a)); for (n=2, nn, my(x = a + a>>1); if (n%2, a = bitor(x, a%2), a = x); listput(va, a); ); Vec(va); } \\ Michel Marcus, May 03 2020
CROSSREFS
KEYWORD
nonn,base
AUTHOR
Simon Strandgaard, Mar 27 2020
STATUS
approved