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

 

Logo

Annual appeal: Please make a donation to keep the OEIS running! Over 6000 articles have referenced us, often saying "we discovered this result with the help of the OEIS".
Other ways to donate

Hints
(Greetings from The On-Line Encyclopedia of Integer Sequences!)
A242793 The minimal integer x such that each of the six integers x, x+1, x+2, x+4, x+5, x+6 is squarefree with exactly n prime divisors. 4
213, 73293, 9743613, 6639266409 (list; graph; refs; listen; history; text; internal format)
OFFSET

2,1

COMMENTS

This is the next step in my project to study the distribution of increasingly extensive clusters of squarefree integers with fixed number of prime divisors: triplets x,x+1,x+2 were investigated in A242492 and here we study sextets x,x+1,x+2,x+4,x+5,x+6 with a central gap x+3, since x+3 must be divisible by the square 4.

The term 6639266409 required 30 hours of CPU time on an iMac with Intel i7 Quadcore CPU running OS X Lion.

LINKS

Table of n, a(n) for n=2..5.

EXAMPLE

213=3*71, 214=2*107, 215=5*43, 217=7*31, 218=2*109, 219=3*73;

73293=3*11*2221, 73294=2*13*2819, 73295=5*107*137,

73297=7*37*283, 73298=2*67*547, 73299=3*53*461;

9743613=3*11*503*587, 9743614=2*59*71*1163, 9743615= 5*7*167*1667, 9743617=13*37*47*431, 9743618=2*17*19*15083, 9743619=3*83*109*359;

6639266409=3*29*109*421*1663, 6639266410=2*5*7*113*839351,

6639266411=17*23*89*101*1889, 6639266413=13*61*79*131*809,

6639266414=2*11*349*857*1009, 6639266415=3*5*73*149*40693.

PROG

(PARI)

{ default(primelimit, 1000M); i=0; j=0; k=0; l=0; m=0; loc=0; lb=2; ub=9*10^9; o=1; while(o<5, o=o+1; for(n=lb, ub, if(issquarefree(n)&&(o==omega(n)), loc=loc+1; if(1==loc, i=n; ); if(2==loc, if(i+1==n, j=n; ); if(i+1<n, loc=1; i=n; ); ); if(3==loc, if(j+1==n, k=n; ); if(j+1<n, loc=1; i=n; ); ); if(4==loc, if(k+2==n, l=n; ); if(k+2<n, loc=1; i=n; ); ); if(5==loc, if(l+1==n, m=n; ); if(l+1<n, loc=1; i=n; ); ); if(6==loc, if(m+1==n, print1(i, ", "); lb=i+1; loc=0; break(1); ); if(m+1<n, loc=1; i=n; ); ); ); ); ); }

CROSSREFS

Cf. A242492 (triplets) and A242804, A242805, A242806, A242829, and also A068088.

Sequence in context: A092796 A280898 A180395 * A242804 A076159 A258961

Adjacent sequences:  A242790 A242791 A242792 * A242794 A242795 A242796

KEYWORD

hard,more,nonn

AUTHOR

Daniel Constantin Mayer, May 22 2014

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 | More pages
The OEIS Community | Maintained by The OEIS Foundation Inc.

License Agreements, Terms of Use, Privacy Policy .

Last modified November 20 13:59 EST 2017. Contains 294972 sequences.