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Indices of prime terms in A254077.
3

%I #45 Jul 13 2024 17:08:03

%S 2,3,10,13,21,24,33,43,46,58,61,70,75,90,97,102,111,120,133,138,141,

%T 155,162,178,187,192,200,209,214,219,247,255,262,265,286,289,302,312,

%U 319,339,346,349,366,376,392,395,413,428,435,444,449,468,471,483,496

%N Indices of prime terms in A254077.

%C It would be nice to have a definition for this sequence which was independent of A254077.

%C From _John Mason_, Apr 15 2015: (Start)

%C Apparently, taking into account the first 675025 terms, corresponding to the first 20 million terms of A254077, a(n) divided by n-th prime A000040(n) is converging to 2. Here is the tail of this calculation:

%C n a(n) prime ratio

%C 675016 19999695 10167763 1.966971004

%C 675017 19999723 10167779 1.966970663

%C 675018 19999766 10167799 1.966971023

%C 675019 19999771 10167803 1.966970741

%C 675020 19999787 10167809 1.966971154

%C 675021 19999790 10167811 1.966971062

%C 675022 19999903 10167881 1.966968634

%C 675023 19999974 10167917 1.966968652

%C 675024 19999985 10167919 1.966969347

%C 675025 19999988 10167923 1.966968869

%C (End)

%C From _John Mason_, May 26 2016: (Start)

%C With respect to the previous observation, apparently, taking into account the first 26694011 terms, corresponding to the first 10^9 terms of A254077, a(n) divided by n-th prime A000040(n) is converging to just under 2. Here is the tail of this calculation:

%C n a(n) prime ratio

%C 26694004 999999729 506784809 1.9732235679542636

%C 26694005 999999770 506784833 1.9732235554097570

%C 26694006 999999827 506784857 1.9732235744368345

%C 26694007 999999857 506784881 1.9732235401868667

%C 26694008 999999915 506784917 1.9732235144638293

%C 26694009 999999941 506784919 1.9732235579804220

%C 26694010 999999946 506784923 1.9732235522720947

%C 26694011 999999967 506784937 1.9732235391992323

%C (End)

%H Ray Chandler and John P. Linderman, <a href="/A256213/b256213.txt">Table of n, a(n) for n = 1..42315</a> [First 10000 terms from Ray Chandler]

%H John Mason, <a href="https://oeis.org/A256213/a256213.zip">The first 675025 terms (zipped file)</a>

%t f[n_] := Block[{s = Range@ n, j, k}, For[k = 4, k <= n, k++, j = 4; While[Nand[GCD[j, s[[k - 2]]] > GCD[j, s[[k - 1]]], !MemberQ[Take[s, k - 1], j]], j++]; s[[k]] = j]; s]; Position[f@ 500, _?PrimeQ] // Flatten (* _Michael De Vlieger_, Apr 15 2015 *)

%o (Haskell)

%o a256213 n = a256213_list !! (n-1)

%o a256213_list = filter ((== 1) . a010051' . a254077) [1..]

%o -- _Reinhard Zumkeller_, May 05 2015

%Y Cf. A254077, A251239, A010051.

%K nonn

%O 1,1

%A _N. J. A. Sloane_, Mar 26 2015