How many numbers are the same for 1,4,7,10,..., 1000 and 1,11,21,31.1001?

How many numbers are the same for 1,4,7,10,..., 1000 and 1,11,21,31.1001?

The law of 1,4,7,10,..., 1000 is 3 * n + 1, (n = 0,1,2,3... 333)
The law of 1,11,21,31.1001 is 10 * m + 1, (M = 0,1,2,3... 100)
For the same number, 3 * n + 1 = 10 * m + 1, that is, M = 3 * n / 10, (M and N are integers)
Therefore, M = 3 * n / 10 can be an integer only when n = 10,20,30,..., 300310320330
Then there are 33 numbers in n = 10, 20, 30, 300310320330
The answer is 33

How many numbers appear simultaneously in the following two series 1, 4, 7, 10.1000 and 1, 11, 21, 31.1001?

Sequence 1: 1,4,7,10 one thousand
→Am=1+3(m-1)=3m-2
∴3m-2≤1000→m≤334
Sequence 2: 1,11,21,31 one thousand and one
→Bn=1+10(n-1)=10n-9
∴10n-9≤1001→n≤101
∴Am=Bn→3m-2=10n-9
∴m=(10n-7)/3 (m,n€N*)
The values of N are: 1,4,7,10
The sequence of values of N: CQ = 3q-2
∴n≤101→3q-2≤101
∴q≤103/3→qmax=34
There are 34 identical terms between AM and BN