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

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, 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, 14, 18, 2, 6, 2, 12, 16, 4, 6, 6, 2, 6, 26, 2, 8, 10, 4, 10, 4

Offset

1,1

Comments

Number of entries in {x,..} such that pi(x) = prime(n).

Links

Amiram Eldar, Table of n, a(n) for n = 1..10000

Formula

a(n) = Card{x; A000720(x) = A000040(n)}.

a(n) = A072677(n) - A006450(n).

Example

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).

Mathematica

Table[Prime[Prime[n]+1]-Prime[Prime[n]], {n, 1, 256}]
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 *)

Prog

(PARI) a(n) =  prime(1+prime(n)) - prime(prime(n)); \\ Michel Marcus, Dec 11 2013

Crossrefs

Cf. A000040, A000720, A006450, A072677, A073123.

Sequence in context: A114005 A103794 A273258 * A278260 A070877 A156717

Adjacent sequences: A073121 A073122 A073123 * A073125 A073126 A073127

Keyword

nonn

Author

Labos Elemer, Jul 16 2002

Extensions

More terms from Michel Marcus, Dec 11 2013

Status

approved