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%I A115319 #11 Nov 15 2021 09:04:48
%S A115319 1,2,8,5,6,3,14,4,11,7,12,9,20,10,17,13,18,15,26,16,23,19,25,21,22,24,
%T A115319 27,28,29,30,31,32,33,34,37,35,36,40,42,43,39,41,38,46,48,49,45,51,54,
%U A115319 55,57,58,44,61,63,64,53,67,52,69,47,72,56,75,76,78,60,62,81,82,50,85
%N A115319 a(n) = A115318(A115318(n)).
%C A115319 Inverse integer permutation of A115317.
%H A115319 <a href="/index/Per#IntegerPermutation">Index entries for sequences that are permutations of the natural numbers</a>
%F A115319 A115316(a(n)) = a(A115316(n)) = A115318(n).
%t A115319 nmax = 72;
%t A115319 nn = nmax + 15; (* estimated length of A115316 - should be increased in case of message "NotFound" in the output *)
%t A115319 np = Ceiling[nn/3] + 1;
%t A115319 nc = Ceiling[(2/3) nn];
%t A115319 pp = Prime[Range[np]];
%t A115319 cc = Partition[Select[Range[FindRoot[n == nc + PrimePi[n] + 1, {n, nc, 2nc}][[1, 2]] // Floor], CompositeQ], 2];
%t A115319 A115316 = Join[{1}, Riffle[pp, cc] // Flatten][[1 ;; nn]];
%t A115319 A115318[n_] := FirstPosition[A115316, n][[1]];
%t A115319 a[n_] := A115318[A115318[n]];
%t A115319 Table[a[n], {n, 1, nmax}] (* _Jean-François Alcover_, Nov 15 2021 *)
%Y A115319 Cf. A115316, A115317, A115318.
%K A115319 nonn
%O A115319 1,2
%A A115319 _Reinhard Zumkeller_, Jan 20 2006

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