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A073124 a(n) = prime(1+prime(n)) - prime(prime(n)).

%I A073124 #20 Feb 15 2025 09:37:00
%S A073124 2,2,2,2,6,2,2,4,6,4,4,6,2,2,12,10,4,10,6,6,6,8,2,2,12,10,6,6,2,2,10,
%T A073124 4,14,12,4,4,10,4,6,2,6,4,10,10,12,6,4,14,6,4,10,12,8,4,6,24,10,6,2,8,
%U A073124 14,18,2,6,2,12,16,4,6,6,2,6,26,2,8,10,4,10,4
%N A073124 a(n) = prime(1+prime(n)) - prime(prime(n)).
%C A073124 Number of entries in {x,..} such that pi(x) = prime(n).
%H A073124 Amiram Eldar, <a href="/A073124/b073124.txt">Table of n, a(n) for n = 1..10000</a>
%F A073124 a(n) = Card{x; A000720(x) = A000040(n)}.
%F A073124 a(n) = A072677(n) - A006450(n).
%e A073124 For n = 25: prime(25) = 97, pi(x) = 97 holds for 12 numbers x: {509, 510, 511, 512, 513, 514, 515, 516, 517, 518, 519, 520} so a(25) = 12. The largest 520 = A073123(25), and the smallest = A006450(25).
%t A073124 Table[Prime[Prime[n]+1]-Prime[Prime[n]], {n, 1, 256}]
%t A073124 seq[max_] := Module[{p = Prime[Range[max + 1]], m = PrimePi[max], ind}, ind = Prime[Range[m]]; p[[ind + 1]] - p[[ind]]]; seq[400] (* _Amiram Eldar_, Feb 15 2025 *)
%o A073124 (PARI) a(n) =  prime(1+prime(n)) - prime(prime(n)); \\ _Michel Marcus_, Dec 11 2013
%Y A073124 Cf. A000040, A000720, A006450, A072677, A073123.
%K A073124 nonn
%O A073124 1,1
%A A073124 _Labos Elemer_, Jul 16 2002
%E A073124 More terms from _Michel Marcus_, Dec 11 2013