login
This site is supported by donations to The OEIS Foundation.

 

Logo


Hints
(Greetings from The On-Line Encyclopedia of Integer Sequences!)
A194585 Starting points of stapled intervals of length 17. 3
2184, 27830, 32214, 57860, 62244, 87890, 92274, 117920, 122304, 147950, 152334, 177980, 182364, 208010, 212394, 238040, 242424, 268070, 272454, 298100, 302484, 328130, 332514, 358160, 362544, 388190, 392574, 418220, 422604, 448250 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,1

COMMENTS

"Stapled" intervals are defined in A090318. They are at least of length 17, and those of this minimal length are listed here. Therefore, this is not only a subsequence of A130173, but also of A130171.

From Fidel I. Schaposnik, Aug 16 2014: (Start)

Let S be the set of distinct prime factors appearing in the factorization of at least two different numbers in the range [a,b], and m the product of all the elements in S.

Then it is clear that if [a,b] is a stapled interval, so is [m+a,m+b].

Moreover, if a > m then the range [a-m,b-m] is also a stapled interval of the same length, so we can group the stapled intervals of a given length in "chains".

To prove the g.f., note that S cannot contain any prime number greater or equal to b-a+1, so for stapled intervals of length 17 the maximum value of m is m = 2*3*5*7*11*13 = 30030.

Then any stapled interval of length 17 must belong to a chain whose first element is at most 30030, and the only stapled intervals in this range are [2184,2200] and [27830,27846].

The g.f. encompasses both these chains, namely a(2*n+1) = 2184 + 30030*n and a(2*n+2) = 27830 + 30030*n.

(End)

LINKS

Fidel I. Schaposnik, Table of n, a(n) for n = 1..666

FORMULA

From Colin Barker, Aug 16 2014: (Start)

a(n) = (-15031+10631*(-1)^n+30030*n)/2.

a(n) = a(n-1)+a(n-2)-a(n-3).

G.f.: 2*x*(1100*x^2+12823*x+1092) / ((x-1)^2*(x+1)). (End)

PROG

(PARI) {u=vector(17, j, 1); v=vector(17, j, j); for(k=2, 1e9, nextprime(k)<k+17 & (v+=u*(-v[1]+k=precprime(k+17))) & next; v+=u; for(j=k, k+16, vecsort(gcd(j, v), , 8)[2]<j | next(2)); print1(k", "))}

CROSSREFS

Cf. A090318, A130170, A130171, A130173.

Sequence in context: A130170 A090318 A130171 * A107657 A002521 A059757

Adjacent sequences:  A194582 A194583 A194584 * A194586 A194587 A194588

KEYWORD

nonn

AUTHOR

M. F. Hasler, Oct 14 2011

STATUS

approved

Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Style Sheet | Transforms | Superseeker | Recent
The OEIS Community | Maintained by The OEIS Foundation Inc.

License Agreements, Terms of Use, Privacy Policy. .

Last modified March 23 16:52 EDT 2019. Contains 321432 sequences. (Running on oeis4.)