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

 

Logo


Hints
(Greetings from The On-Line Encyclopedia of Integer Sequences!)
A244620 Initial terms of Erdős-Wood intervals of length 22. 2
3521210, 6178458, 13220900, 15878148, 22920590, 25577838, 32620280, 35277528, 42319970, 44977218, 52019660, 54676908, 61719350, 64376598, 71419040, 74076288, 81118730, 83775978, 90818420, 93475668, 100518110, 103175358, 110217800, 112875048, 119917490 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,1

COMMENTS

By definition of the intervals in A059756, these are numbers that start a sequence of 23 consecutive integers such that none of the 23 integers is coprime to the first and also coprime to the last integer of the interval.

Hence each initial term of an Erdős-Wood interval is the initial term of a stapled interval of length A059756(n) + 1 (see definition in A090318). - Christopher Hunt Gribble, Dec 02 2014

LINKS

Christopher Hunt Gribble, Table of n, a(n) for n = 1..1000

Wikipedia, Erdős-Woods number

FORMULA

a(1) = A059757(2).

From Christopher Hunt Gribble, Dec 02 2014: (Start)

a(1) = A130173(524).

a(2*n+1) = 3521210 + 9699690*n.

a(2*n+2) = 6178458 + 9699690*n.

a(n) = (-4849867 - 2192597*(-1)^n + 9699690*n)/2.

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

G.f.: (3521232*x^2+2657248*x+3521210) / ((x-1)^2*(x+1)). (End)

EXAMPLE

3521210 = 2*5*7*11*17*269 and 3521210+22 = 3521232 = 2^4 * 3^4 * 11 * 13 * 19, and all numbers in [3521210,3521232] have at least one prime factor in {2, 3, 5, 7, 11, 13, 17, 19, 269}. Therefore 3521210 is in the list.

MAPLE

isEWood := proc(n, ewlength)

    local nend, fsn, fsne, fsall, fsk ;

    nend := n+ewlength ;

    fsn := numtheory[factorset](n) ;

    fsne := numtheory[factorset](nend) ;

    fsall := fsn union fsne ;

    for k from n to nend do

        fsk := numtheory[factorset](k) ;

        if fsk intersect fsall = {} then

            return false;

        end if;

    end do:

    return true;

end proc:

for n from 2 do

    if isEWood(n, 22) then

        print(n) ;

    end if;

end do:

CROSSREFS

Cf. A059757, A194585, A090318, A130173.

Sequence in context: A083624 A237006 A209785 * A202570 A209857 A107349

Adjacent sequences:  A244617 A244618 A244619 * A244621 A244622 A244623

KEYWORD

nonn

AUTHOR

R. J. Mathar, Jul 02 2014

EXTENSIONS

More terms from Christopher Hunt Gribble, Dec 03 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
The OEIS Community | Maintained by The OEIS Foundation Inc.

License Agreements, Terms of Use, Privacy Policy. .

Last modified October 21 11:42 EDT 2019. Contains 328296 sequences. (Running on oeis4.)