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A251239 Indices of prime numbers in A098550.

%I A251239 #27 Jul 26 2024 05:21:47
%S A251239 2,3,9,15,22,23,30,43,51,61,62,79,87,88,101,114,127,132,142,153,158,
%T A251239 167,175,194,204,215,222,233,238,247,274,283,296,301,324,329,338,355,
%U A251239 364,375,386,393,414,423,430,435,452,479,490,497,506,523,528,541,550
%N A251239 Indices of prime numbers in A098550.
%C A251239 It is conjectured that every prime appears in A098550, and if so then A098550(a(n)) = A000040(n). [Comment edited by _N. J. A. Sloane_, Dec 15 2014] [It is now known that every prime appears in A098550, although it is not known that they appear in their right order. - _N. J. A. Sloane_, Dec 25 2014]
%C A251239 A010051(A098550(a(n))) = 1; A049084(A098550(a(n))) > 0.
%C A251239 Conjecture: a(n) = A251541(n) + 2 for n > 4. - _Reinhard Zumkeller_, Dec 16 2014
%C A251239 A253049(n) = A098550(a(n)+1). - _Reinhard Zumkeller_, Dec 29 2014
%H A251239 Reinhard Zumkeller, <a href="/A251239/b251239.txt">Table of n, a(n) for n = 1..10000</a>
%t A251239 a098550[lst_List] :=
%t A251239 Block[{k = 4},
%t A251239   While[GCD[lst[[-2]], k] == 1 || GCD[lst[[-1]], k] > 1 ||
%t A251239     MemberQ[lst, k], k++]; Append[lst, k]];
%t A251239 a251239[n_] :=
%t A251239 Flatten@Position[Nest[a098550, {1, 2, 3}, n], _Integer?PrimeQ]; a251239[550] (* _Michael De Vlieger_, Dec 23 2014, based on _Robert G. Wilson v_ at A098550 *)
%o A251239 (Haskell)
%o A251239 a251239 n = a251239_list !! (n-1)
%o A251239 a251239_list = filter ((== 1) . a010051' . a098550) [1..]
%Y A251239 Cf. A098550, A010051, A049084, A251392, A247253 (first differences), A251595, A251541, A253049, A253048.
%Y A251239 This is a subsequence of A251391 and A251241,
%K A251239 nonn
%O A251239 1,1
%A A251239 _Reinhard Zumkeller_, Dec 02 2014