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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
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
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
KEYWORD
nonn
AUTHOR
R. J. Mathar, Jul 02 2014
EXTENSIONS
More terms from Christopher Hunt Gribble, Dec 03 2014
STATUS
approved