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A298861 Rank of n-th prime when all the primes and twice-primes are jointly ranked.

%I A298861 #8 Feb 14 2018 08:23:34
%S A298861 1,2,4,6,8,9,11,12,14,16,17,19,21,22,24,25,27,28,30,31,32,34,36,38,40,
%T A298861 41,42,44,45,46,49,50,52,53,56,57,58,60,62,63,65,66,67,68,70,71,74,77,
%U A298861 79,80,81,82,83,84,86,88,89,90,92,94,95,96,99,100,101
%N A298861 Rank of n-th prime when all the primes and twice-primes are jointly ranked.
%H A298861 Clark Kimberling, <a href="/A298861/b298861.txt">Table of n, a(n) for n = 1..1000</a>
%e A298861 A001751 = ordered sequence of primes and twice-primes: 2,3,4,5,6,7,10,... in which the primes occupy ranks 1,2,4,6,...
%t A298861 z = 1000; u = Prime[Range[z]]; w = Take[Union[u, 2 u], z];
%t A298861 p[n_] := If[MemberQ[u, w[[n]]], 0, 1];
%t A298861 Take[w, z];  (* A001751 *)
%t A298861 t = Table[p[n], {n, 1, z}];
%t A298861 Flatten[Position[t, 0]];  (* A298861 *)
%t A298861 Flatten[Position[t, 1]];  (* A298862 *)
%Y A298861 Cf. A000040, A001751, A298862 (complement).
%K A298861 nonn,easy
%O A298861 1,2
%A A298861 _Clark Kimberling_, Feb 13 2018