The author makes a fundamental error at the very beginning, but he is not alone. Gail Howard and Ken Silver make the same mistake.
He says "All numbers have an even chance of being drawn: nothing could be further from the truth. If that is truly the case we should see numbers like 1-2-3-4-5-6 or 54-55-56-57-58-59 being drawn all the time."
That is an incorrect conclusion. Let us start with the premise that all numbers are equally likely to be drawn and try to draw a correct conclusion.
The author seems to be talking about a 6/59 lottery and six-number sequences. There are 54 such sequences but 45,057,474 possible combinations that could be drawn, so that if all numbers and combinations are equally likely to be drawn the chance of drawing a sequence at random is 54 in 45,057,474 or 1 in 834,397.66+. That means a sequence could be expected to come up an average of once in 834,398 drawings. For a lottery that has two drawings a week that would be an average of once in every 8,023 years. The reason that we do not see sequences being drawn is not because they are less likely to be drawn than other combinations but because there are so few of them. There is only one reported case of a sequence being drawn in a lottery: 14-15-16-17-18 in Florida Fantasy Five.