What are the next two numbers in this sequence? 7, 14, 17, 21, 27, 28, 35, 37,…

Concept: This is a number series of natural numbers, listed in ascending order, where each term satisfies at least one of two conditions: (i) it is a multiple of 7, or (ii) it contains the digit 7 anywhere in it. A term needs to satisfy only one of the two conditions to be included.

Application:

1. The last given term is 37, which contains the digit 7 (condition ii).

2. Check the natural numbers after 37 one by one against the two conditions: 38, 39, 40 and 41 are not multiples of 7 and do not contain the digit 7, so none of them qualify.

3. 42 = 7 × 6 is a multiple of 7, so it qualifies as the next term.

4. 43, 44, 45 and 46 are neither multiples of 7 nor contain the digit 7, so none of them qualify.

5. 47 contains the digit 7, so it qualifies as the term right after 42.

6. Hence the next two numbers in the sequence are 42 and 47.

Cross-check: The same rule explains every term already given: 21 = 3 × 7, 28 = 4 × 7 and 35 = 5 × 7 are multiples of 7, while 17, 27 and 37 contain the digit 7. The identical two-condition pattern, extended in ascending order past 37, gives 42 and then 47, confirming the result.