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 A251417 Lengths of runs of identical terms in A251416. 12
 1, 1, 1, 5, 1, 5, 1, 6, 1, 7, 1, 12, 8, 10, 1, 17, 8, 1, 13, 13, 13, 5, 10, 11, 5, 9, 8, 19, 10, 11, 7, 11, 5, 9, 27, 9, 13, 5, 23, 5, 9, 17, 9, 11, 11, 7, 21, 9, 7, 5, 17, 27, 11, 7, 9, 17, 5, 13, 9, 21, 11, 7, 13, 9, 9 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,4 COMMENTS It would be nice to have an alternative description of this sequence, one that is not based on A098550. It appears (conjecture) that a(n)>1 for n>18. - Alexander R. Povolotsky, Dec 07 2014 Conjecture: a(n) = A247253(n-5) for n>12. - Reinhard Zumkeller, Dec 07 2014 The previous conjecture is equivalent to the statement that A251416(n) lists all primes and only primes after a(30)=18. - M. F. Hasler, Dec 08 2014 LINKS Reinhard Zumkeller, Table of n, a(n) for n = 1..10000 FORMULA Let f(n)=A098551(A251595(n)). Then one can prove that A251417(n) = f(n) - f(n-1), n>=2. - Vladimir Shevelev, Dec 09 2014 EXAMPLE See A251595. MATHEMATICA termsOfA251416 = 700; 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}, termsOfA251416 - 3]; b = 2; b[n_] := b[n] = For[k = b[n-1], True, k++, If[FreeQ[A098550[[1 ;; n]], k], Return[k]]]; A251416 = Array[b, termsOfA251416]; Length /@ Split[A251416] (* Jean-François Alcover, Aug 01 2018, after Robert G. Wilson v *) PROG (Haskell) import Data.List (group) a251417 n = a251417_list !! (n-1) a251417_list = map length \$ group a251416_list -- Reinhard Zumkeller, Dec 05 2014 CROSSREFS Cf. A098550, A251416, A251595, A247253. Sequence in context: A056957 A224834 A095118 * A100947 A096940 A141345 Adjacent sequences:  A251414 A251415 A251416 * A251418 A251419 A251420 KEYWORD nonn AUTHOR N. J. A. Sloane, Dec 03 2014 STATUS approved

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Last modified April 21 23:52 EDT 2021. Contains 343156 sequences. (Running on oeis4.)