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