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A064955 Position of n-th prime in A064413.

%I A064955 #20 Apr 22 2025 15:26:01
%S A064955 2,5,10,14,20,28,33,37,43,57,61,67,74,81,89,100,107,115,128,134,138,
%T A064955 151,160,167,182,189,197,203,207,216,236,253,259,264,279,287,297,305,
%U A064955 314,328,336,344,363,371,377,381,401,420,430,438,444,458,462,474,487,501,510,517,530,540,549,557,581,587,599,606,629,639,655,664,670,681,699,707,724,730,736,756,766,781,798,802,814,819,833,848,857,874,882,889,898,911,927,942,953,961,971,997,1004,1029,1041,1059,1072,1080,1087,1099,1118,1135,1142,1150,1156,1175,1181,1190,1203,1223,1232,1242,1249,1258,1266,1287,1298,1306,1324,1350,1357,1378,1391,1398,1410,1425,1433,1442,1456,1470,1478,1504,1516,1542,1546,1564,1568,1578,1586,1610,1626,1638,1646,1652,1680,1686,1693,1702,1734,1739,1760
%N A064955 Position of n-th prime in A064413.
%C A064955 It can be shown that this sequence is monotonic.
%C A064955 A073734(a(n)) = A000040(n) for n > 1. - _Reinhard Zumkeller_, Sep 17 2001
%H A064955 Reinhard Zumkeller, <a href="/A064955/b064955.txt">Table of n, a(n) for n = 1..10000</a>
%H A064955 J. C. Lagarias, E. M. Rains and N. J. A. Sloane, <a href="http://arXiv.org/abs/math.NT/0204011">The EKG sequence</a>, Exper. Math. 11 (2002), 437-446.
%H A064955 <a href="/index/Ed#EKG">Index entries for sequences related to EKG sequence</a>
%F A064955 a(n) = A064664(A000040(n)).
%t A064955 ekg[s_] := Block[{m = s[[-1]], k = 3}, While[MemberQ[s, k] || GCD[m, k] == 1, k++]; Append[s, k]];
%t A064955 A064413 = Nest[ekg, {1, 2}, 1000];
%t A064955 Position[A064413, _?PrimeQ] // Flatten (* _Jean-François Alcover_, Nov 03 2018, after _Robert G. Wilson v_ in 064413 *)
%o A064955 (Haskell)
%o A064955 import Data.List (elemIndex)
%o A064955 import Data.Maybe (fromJust)
%o A064955 a064955 n = a064955_list !! (n-1)
%o A064955 a064955_list =
%o A064955    map ((+ 1) . fromJust . (`elemIndex` a064413_list)) a000040_list
%o A064955 -- _Reinhard Zumkeller_, Sep 17 2001
%Y A064955 Cf. A000040, A064413, A064425, A064664, A073734.
%Y A064955 Setwise difference A383294 \ A383295.
%K A064955 nonn
%O A064955 1,1
%A A064955 _N. J. A. Sloane_, Oct 30 2001