10: 6 8 8 = 8 6 * 8 18: 13 16 15 = 16 13 * 15 28: 22 26 24 = 26 22 * 24 40: 33 38 35 = 38 33 * 35 54: 46 52 48 = 52 46 * 48 70: 61 68 63 = 68 61 * 63 88: 78 86 80 = 86 78 * 80 Base: a = x*(x+3) for all x > 1 Digits: a - (x+2), a - 2, a - x 6: 1 3 3 = 3 1 * 3 14: 2 9 4 = 4 2 * 9 26: 3 19 5 = 5 3 * 19 42: 4 33 6 = 6 4 * 33 62: 5 51 7 = 7 5 * 51 86: 6 73 8 = 8 6 * 73 Base: 2 * (x^2 + x + 1) for all x > 0 Digits: x, 2 * x^2 + 1, x + 2 14: 2 9 4 = 4 2 * 9 32: 4 18 8 = 8 4 * 18 50: 6 27 12 = 12 6 * 27 68: 8 36 16 = 16 8 * 36 86: 10 45 20 = 20 10 * 45 75: 3 28 9 = 9 3 * 28 Base: (y^4 + y) * x - y^2 for all x > 0, y > 1 Digits: y * x, (y^3 + 1) * x, y^2 * x (These are the only families where the digits have the form b*x c*x d*x for coprime b, c, d.) 6: 1 3 3 = 3 1 * 3 12: 3 7 6 = 7 3 * 6 18: 5 11 9 = 11 5 * 9 24: 7 15 12 = 15 7 * 12 30: 9 19 15 = 19 9 * 15 36: 11 23 18 = 23 11 * 18 42: 13 27 21 = 27 13 * 21 48: 15 31 24 = 31 15 * 24 54: 17 35 27 = 35 17 * 27 60: 19 39 30 = 39 19 * 30 66: 21 43 33 = 43 21 * 33 72: 23 47 36 = 47 23 * 36 78: 25 51 39 = 51 25 * 39 84: 27 55 42 = 55 27 * 42 90: 29 59 45 = 59 29 * 45 96: 31 63 48 = 63 31 * 48 12: 1 4 4 = 4 1 * 4 36: 4 13 12 = 13 4 * 12 60: 7 22 20 = 22 7 * 20 84: 10 31 28 = 31 10 * 28 20: 1 5 5 = 5 1 * 5 80: 5 21 20 = 21 5 * 20 30: 1 6 6 = 6 1 * 6 42: 1 7 7 = 7 1 * 7 56: 1 8 8 = 8 1 * 8 72: 1 9 9 = 9 1 * 9 90: 1 10 10 = 10 1 * 10 Base: a = x * (x + 1) * ((x - 1) * y + 1) for all x > 1, y >= 0 Digits: x * y + 1, x^2 * y + x + 1, a/x (Notice: y = 0 yields a subset of the 1ab VNs) 6: 1 3 3 = 3 1 * 3 12: 3 7 6 = 7 3 * 6 18: 5 11 9 = 11 5 * 9 24: 7 15 12 = 15 7 * 12 30: 9 19 15 = 19 9 * 15 36: 11 23 18 = 23 11 * 18 42: 13 27 21 = 27 13 * 21 48: 15 31 24 = 31 15 * 24 54: 17 35 27 = 35 17 * 27 60: 19 39 30 = 39 19 * 30 66: 21 43 33 = 43 21 * 33 72: 23 47 36 = 47 23 * 36 78: 25 51 39 = 51 25 * 39 84: 27 55 42 = 55 27 * 42 90: 29 59 45 = 59 29 * 45 96: 31 63 48 = 63 31 * 48 6: 1 2 4 = 2 1 * 4 21: 7 11 14 = 11 7 * 14 36: 13 20 24 = 20 13 * 24 51: 19 29 34 = 29 19 * 34 66: 25 38 44 = 38 25 * 44 81: 31 47 54 = 47 31 * 54 96: 37 56 64 = 56 37 * 64 16: 5 7 12 = 7 5 * 12 44: 17 23 33 = 23 17 * 33 72: 29 39 54 = 39 29 * 54 100: 41 55 75 = 55 41 * 75 30: 11 14 24 = 14 11 * 24 75: 31 39 60 = 39 31 * 60 48: 19 23 40 = 23 19 * 40 70: 29 34 60 = 34 29 * 60 96: 41 47 84 = 47 41 * 84 Base: a = x * ((2 * x - 1) * y - 3) for all x > 1, y > 0 except (x,y) = (2,1) Digits: x * (x - 1) * y - 2 * x + 1, x^2 * y - 2 * x - 1, a * (x - 1) / x (Notice: y = 1 yields a subset of the previous family.)