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A251417 Lengths of runs of identical terms in A251416.

%I A251417 #25 Aug 01 2018 09:21:25
%S A251417 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,
%T A251417 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,
%U A251417 13,9,21,11,7,13,9,9
%N A251417 Lengths of runs of identical terms in A251416.
%C A251417 It would be nice to have an alternative description of this sequence, one that is not based on A098550.
%C A251417 It appears (conjecture) that a(n)>1 for n>18. - _Alexander R. Povolotsky_, Dec 07 2014
%C A251417 Conjecture: a(n) = A247253(n-5) for n>12. - _Reinhard Zumkeller_, Dec 07 2014
%C A251417 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
%H A251417 Reinhard Zumkeller, <a href="/A251417/b251417.txt">Table of n, a(n) for n = 1..10000</a>
%F A251417 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
%e A251417 See A251595.
%t A251417 termsOfA251416 = 700;
%t A251417 f[lst_List] := Block[{k = 4}, While[GCD[lst[[-2]], k] == 1 || GCD[lst[[-1]], k] > 1 || MemberQ[lst, k], k++]; Append[lst, k]];
%t A251417 A098550 = Nest[f, {1, 2, 3}, termsOfA251416 - 3];
%t A251417 b[1] = 2;
%t A251417 b[n_] := b[n] = For[k = b[n-1], True, k++, If[FreeQ[A098550[[1 ;; n]], k], Return[k]]];
%t A251417 A251416 = Array[b, termsOfA251416];
%t A251417 Length /@ Split[A251416] (* _Jean-François Alcover_, Aug 01 2018, after _Robert G. Wilson v_ *)
%o A251417 (Haskell)
%o A251417 import Data.List (group)
%o A251417 a251417 n = a251417_list !! (n-1)
%o A251417 a251417_list = map length $ group a251416_list
%o A251417 -- _Reinhard Zumkeller_, Dec 05 2014
%Y A251417 Cf. A098550, A251416, A251595, A247253.
%K A251417 nonn
%O A251417 1,4
%A A251417 _N. J. A. Sloane_, Dec 03 2014