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

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, 41, 42, 44, 45, 46, 49, 50, 52, 53, 56, 57, 58, 60, 62, 63, 65, 66, 67, 68, 70, 71, 74, 77, 79, 80, 81, 82, 83, 84, 86, 88, 89, 90, 92, 94, 95, 96, 99, 100, 101

Offset: 1

Author

Clark Kimberling, Feb 13 2018

Keywords

• nonn
• easy

Examples

			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,...
		

Links

• Clark Kimberling, Table of n, a(n) for n = 1..1000

Crossrefs

Cf. A000040, A001751, A298862 (complement).

Programs

Mathematica

z = 1000; u = Prime[Range[z]]; w = Take[Union[u, 2 u], z];
p[n_] := If[MemberQ[u, w[[n]]], 0, 1];
Take[w, z];  (* A001751 *)
t = Table[p[n], {n, 1, z}];
Flatten[Position[t, 0]];  (* A298861 *)
Flatten[Position[t, 1]];  (* A298862 *)