March 20, 2000
Problem of the Month

The Number Sequence Problem
by Lyle Fisher and
William Medigovich

The numbers in the sequence 2, 7, 12, 17, 22, 27, 32, 37, ... increase by 5s.

The numbers in the sequence 3, 10, 17, 24, 31, 38, 45, 52, ... increase by 7s.

What are the first 10 numbers which appear in both sequences?

Solution to the Problem:

Answer: 17, 52, 87, 122, 157, 192, 227, 262, 297, 332

The 2 sequences continue as follows:
2, 7, 12, 17, 22, 27, 32, 37, 42, 47, 52, 57, 62, 67, ...

3, 10, 17, 24, 31, 38, 45, 52, 59, 66, 73, 80, 87, 94, ...

Since 5 and 7 have no common factors, the only values the sequences have in common are 17, plus multiples of 5x7.

A computer program would also be an easy way to solve this problem.

Correctly solved by:

1. Tom Marino	Winchester, VA
2. Sam Stiebel	Winchester, VA
3. Elizabeth Cotter	Oak Hill, VA
4. Richard Mocarski	Winchester, VA
5. Eric Harding	McLean, VA
6. Court Pifer	Winchester, VA
7. Joe Jenkins *	Winchester, VA
8. Chip Schewikarth *	Winchester, VA
9. Chip Crawford	Winchester, VA
10. Kirstine Wynn	Winchester, VA

* Wrote Computer Programs in Pascal to solve the problem

Send any comments or questions to: David Pleacher