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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 (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

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Last modified April 21 01:53 EDT 2021. Contains 343143 sequences. (Running on oeis4.)