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A244620
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Initial terms of Erdős-Wood intervals of length 22.
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2
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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
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OFFSET
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1,1
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COMMENTS
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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
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LINKS
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Christopher Hunt Gribble, Table of n, a(n) for n = 1..1000
Wikipedia, Erdős-Woods number
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FORMULA
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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)
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EXAMPLE
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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.
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MAPLE
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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:
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CROSSREFS
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Cf. A059757, A194585, A090318, A130173.
Sequence in context: A083624 A237006 A209785 * A202570 A209857 A107349
Adjacent sequences: A244617 A244618 A244619 * A244621 A244622 A244623
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KEYWORD
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nonn
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AUTHOR
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R. J. Mathar, Jul 02 2014
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EXTENSIONS
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More terms from Christopher Hunt Gribble, Dec 03 2014
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STATUS
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approved
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