You are given a sequence of numbers as follows:
0,0,3,2,25,24,203,202,_,_,2299,_,...
Given these terms, what are the missing values?
What is the formula for finding the nth term in the sequence?
(In reply to
Puzzle Answer by K Sengupta)
Let the jth term of the sequence be given by S(n).
Then the terms of the given sequence are given by:
S(n) = A(n) - B(n), where:
A(n) = n#, where n# denotes the product of primes <=n
The first 12 terms of n# is given in Sloane's A034386 at oeis.org as:
1, 2, 6, 6, 30, 30, 210, 210, 210, 210, 2310, 2310
B(n) denotes the set of positive integers, given in Sloane's A000027, and the first 12 values are:
1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12
Thus, we must have:
S(1) = 1-1 = 0
S(2) = 2-2 = 0
S(3) = 6-3 = 3
S(4) = 6-4 = 2
S(5) = 30-5 = 25
S(6) = 30-6 = 24
S(7) = 210 - 7 = 203
S(8) = 210 - 8 = 202
S(9) = 210 - 9 = 201
S(10) = 210 -10 = 200
S(11) = 2310 - 11 = 2299
S(12) = 2310 -12 = 2298
Consequently, the required missing terms are:
201, 200, and 2298
Edited on August 19, 2022, 10:37 pm
Explanation to Puzzle Answer
