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 A251416 a(n) = smallest number not in {A098550(1), A098550(2), ..., A098550(n)}. 12
 2, 3, 4, 5, 5, 5, 5, 5, 6, 7, 7, 7, 7, 7, 10, 11, 11, 11, 11, 11, 11, 13, 17, 17, 17, 17, 17, 17, 17, 18, 19, 19, 19, 19, 19, 19, 19, 19, 19, 19, 19, 19, 23, 23, 23, 23, 23, 23, 23, 23, 29, 29, 29, 29, 29, 29, 29, 29, 29, 29, 31 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,1 COMMENTS a(n) = smallest missing number in A098550 once we have found A098550(n). Bradley Klee conjectures that after a(30)=18, all further terms are primes, that every prime appears, and the primes appear in increasing order. REFERENCES Bradley Klee, Posting to Sequence Fans Mailing List, Dec 03 2014 LINKS N. J. A. Sloane and Reinhard Zumkeller, Table of n, a(n) for n = 1..100000 (first 1000 terms from N. J. A. Sloane) FORMULA a(n) = Min{A251546(n), A251549(n)}. - Reinhard Zumkeller, Dec 19 2014 MAPLE # This produces the first 100 terms. Uses b1 = list of terms in A098550, from b-file b2:={\$3..5000}: b3:=[2]: for i from 2 to 100 do b2:=remove('x->x=b1[i]', b2): b3:=[op(b3), b2[1]]; od: b3; MATHEMATICA terms = 100; f[lst_List] := Block[{k = 4}, While[GCD[lst[[-2]], k] == 1 || GCD[lst[[-1]], k] > 1 || MemberQ[lst, k], k++]; Append[lst, k]]; A098550 = Nest[f, {1, 2, 3}, terms-3]; a[1] = 2; a[n_] := a[n] = For[k = a[n - 1], True, k++, If[FreeQ[A098550[[1 ;; n]], k], Return[k]]]; Array[a, terms] (* Jean-François Alcover, Aug 01 2018, after Robert G. Wilson v *) PROG (Haskell) import Data.List (delete) a251416 n = a251416_list !! (n-1) a251416_list = 2 : 3 : f 2 3 [4..] where    f u v ws = h ws where      h (x:xs) = if gcd x u > 1 && gcd x v == 1                    then (head ws) : f v x (delete x ws) else h xs -- Reinhard Zumkeller, Dec 05 2014 CROSSREFS Cf. A098550, A251415. See A251417 for lengths of runs. Cf. A251595 (distinct terms). Cf. A251546, A251549. Sequence in context: A087846 A067854 A194214 * A087829 A078474 A087177 Adjacent sequences:  A251413 A251414 A251415 * A251417 A251418 A251419 KEYWORD nonn AUTHOR N. J. A. Sloane, Dec 03 2014 STATUS approved

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Last modified April 22 07:26 EDT 2021. Contains 343163 sequences. (Running on oeis4.)