A084294 Number of primes in the interval [prime(n),n+prime(n)].

2, 2, 2, 2, 2, 3, 3, 2, 3, 3, 3, 4, 4, 3, 4, 4, 5, 5, 5, 5, 4, 5, 5, 7, 6, 6, 5, 5, 5, 5, 7, 7, 7, 7, 8, 7, 8, 9, 8, 8, 7, 7, 9, 8, 9, 8, 9, 11, 10, 10, 11, 10, 10, 9, 10, 11, 10, 9, 9, 9, 8, 10, 11, 11, 10, 11, 12, 12, 12, 12, 12, 12, 13, 13, 13, 13, 14, 14, 14, 14, 15, 15, 15, 14, 15, 14, 13

Offset

1,1

Links

Table of n, a(n) for n=1..87.

Formula

a(n) = Pi(n+prime(n)) - n + 1 = A000720(n+A000040(n)) - n + 1. [corrected by Michel Marcus, Aug 28 2019]

Mathematica

t[x_] := Table[w, {w, Prime[x], x+Prime[x]}] Table[Count[PrimeQ[t[n]], True], {n, 1, 128}] (* or *) Table[PrimePi[n+Prime[n]]-n+1, {n, 1, 25}];

Prog

(PARI) a(n) = primepi(n+prime(n)) - n + 1; \\ Michel Marcus, Aug 28 2019

Crossrefs

Cf. A000040, A000720, A061067, A061068, A084295.

Sequence in context: A319696 A320111 A234287 * A067752 A229942 A025422

Adjacent sequences: A084291 A084292 A084293 * A084295 A084296 A084297

Keyword

nonn

Author

Labos Elemer, May 27 2003

Status

approved