A256213 Indices of prime terms in A254077.

2, 3, 10, 13, 21, 24, 33, 43, 46, 58, 61, 70, 75, 90, 97, 102, 111, 120, 133, 138, 141, 155, 162, 178, 187, 192, 200, 209, 214, 219, 247, 255, 262, 265, 286, 289, 302, 312, 319, 339, 346, 349, 366, 376, 392, 395, 413, 428, 435, 444, 449, 468, 471, 483, 496

Offset: 1

Author

N. J. A. Sloane, Mar 26 2015

Keywords

• nonn

Comments

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

From John Mason, Apr 15 2015: (Start)

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:

n a(n) prime ratio

675016 19999695 10167763 1.966971004

675017 19999723 10167779 1.966970663

675018 19999766 10167799 1.966971023

675019 19999771 10167803 1.966970741

675020 19999787 10167809 1.966971154

675021 19999790 10167811 1.966971062

675022 19999903 10167881 1.966968634

675023 19999974 10167917 1.966968652

675024 19999985 10167919 1.966969347

675025 19999988 10167923 1.966968869

(End)

From John Mason, May 26 2016: (Start)

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:

n a(n) prime ratio

26694004 999999729 506784809 1.9732235679542636

26694005 999999770 506784833 1.9732235554097570

26694006 999999827 506784857 1.9732235744368345

26694007 999999857 506784881 1.9732235401868667

26694008 999999915 506784917 1.9732235144638293

26694009 999999941 506784919 1.9732235579804220

26694010 999999946 506784923 1.9732235522720947

26694011 999999967 506784937 1.9732235391992323

(End)

Links

• Ray Chandler and John P. Linderman, Table of n, a(n) for n = 1..42315 [First 10000 terms from Ray Chandler]
• John Mason, The first 675025 terms (zipped file)

Crossrefs

Cf. A254077, A251239, A010051.

Programs

Haskell

a256213 n = a256213_list !! (n-1)
a256213_list = filter ((== 1) . a010051' . a254077) [1..]
-- Reinhard Zumkeller, May 05 2015

Mathematica

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 *)