A333589 a(n) = floor(a(n-1)*3/2) bitwise-OR LSB(a(n-1)*n), with a(1)=2 (LSB = Least Significant Bit).
2, 3, 5, 7, 11, 16, 24, 36, 54, 81, 121, 181, 271, 406, 609, 913, 1369, 2053, 3079, 4618, 6927, 10390, 15585, 23377, 35065, 52597, 78895, 118342, 177513, 266269, 399403, 599104, 898656, 1347984, 2021976, 3032964, 4549446, 6824169, 10236253, 15354379, 23031569, 34547353, 51821029, 77731543, 116597315
Offset: 1
Examples
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
Programs
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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 *)
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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 -
Ruby
values = [2]; 100.times { |index| x = values.last; values << ((x + (x>>1)) | (x&1&index)) }; p values
Formula
a(n) = floor(a(n-1)*3/2) bitwise-OR LSB(a(n-1)*n), with a(1)=2 (LSB = Least Significant Bit).