A251239 - OEIS

%I #27 Jul 26 2024 05:21:47

%S 2,3,9,15,22,23,30,43,51,61,62,79,87,88,101,114,127,132,142,153,158,

%T 167,175,194,204,215,222,233,238,247,274,283,296,301,324,329,338,355,

%U 364,375,386,393,414,423,430,435,452,479,490,497,506,523,528,541,550

%N Indices of prime numbers in A098550.

%C 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 A010051(A098550(a(n))) = 1; A049084(A098550(a(n))) > 0.

%C Conjecture: a(n) = A251541(n) + 2 for n > 4. - _Reinhard Zumkeller_, Dec 16 2014

%C A253049(n) = A098550(a(n)+1). - _Reinhard Zumkeller_, Dec 29 2014

%H Reinhard Zumkeller, <a href="/A251239/b251239.txt">Table of n, a(n) for n = 1..10000</a>

%t a098550[lst_List] :=

%t Block[{k = 4},

%t   While[GCD[lst[[-2]], k] == 1 || GCD[lst[[-1]], k] > 1 ||

%t     MemberQ[lst, k], k++]; Append[lst, k]];

%t a251239[n_] :=

%t 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 (Haskell)

%o a251239 n = a251239_list !! (n-1)

%o a251239_list = filter ((== 1) . a010051' . a098550) [1..]

%Y Cf. A098550, A010051, A049084, A251392, A247253 (first differences), A251595, A251541, A253049, A253048.

%Y This is a subsequence of A251391 and A251241,

%K nonn

%O 1,1

%A _Reinhard Zumkeller_, Dec 02 2014