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A084294
Number of primes in the interval [prime(n),n+prime(n)].
0
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
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
KEYWORD
nonn
AUTHOR
Labos Elemer, May 27 2003
STATUS
approved