OFFSET
1,1
COMMENTS
The sequence is strongly associated with A072752.
In A072752, you are looking for a maximum sized set of consecutive numbers where none are counted by Euler's phi(3*5*7*...*Pn); this sequence looks for a minimum sized set of consecutive numbers where all the numbers counted by Euler are included.
One candidate for A (not necessarily of minimum size) is the set {1, 2, 3,..., 3*5*..*Pn}, which has the requested number of coprime elements. This yields the simple upper bound a(n) <= A070826(n+1). - R. J. Mathar, May 03 2017
FORMULA
Let A = { set of any k consecutive integers}, |A| its size.
Let B = {x IN A | gcd(x, 3*5*7...Prime(n))=1}.
Condition: |B| = phi(3*5*7...Prime(n))= A005867(n+1).
a(n) = minimum(|A|) which meets the above condition.
EXAMPLE
a(1)=2, phi(3) = 2, A={1,2 }, B={1,2}, |B|=2 gcd(1,3) = 1; gcd(2,3) = 1; minimum(|A|) = 2.
a(2)=13, phi(3*5) = 8, A={7,8,9,10,...,19}, B={7, 8, 11, 13, 14, 16, 17, 19}, |B|=8, A was chosen so |A| is a minimum.
CROSSREFS
KEYWORD
hard,more,nonn
AUTHOR
John F. Morack, Dec 22 2013
EXTENSIONS
Edited by R. J. Mathar, May 03 2017
STATUS
approved