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A109579 Sum([pi(j+1)-pi(j)][prime(j+1)-prime(j)],j=1..n), where pi(k) is the number of prime numbers less than or equal to k and prime(k) is the k-th prime. 1
1, 3, 3, 7, 7, 11, 11, 11, 11, 13, 13, 17, 17, 17, 17, 23, 23, 29, 29, 29, 29, 33, 33, 33, 33, 33, 33, 35, 35, 49, 49, 49, 49, 49, 49, 55, 55, 55, 55, 61, 61, 71, 71, 71, 71, 83, 83, 83, 83, 83, 83, 85, 85, 85, 85, 85, 85, 91, 91, 93, 93, 93, 93, 93, 93, 107, 107, 107, 107, 111 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,2

LINKS

Table of n, a(n) for n=1..70.

EXAMPLE

a(2)=3 because pi(1)=0,p(2)=1,p(3)=2,prime(1)=2,prime(2)=3,prime(3)=5 and so a(2)=(1-0)(3-2)+(2-1)(5-3)=1+2=3.

MAPLE

with(numtheory): a:=n->sum((pi(k+1)-pi(k))*(ithprime(k+1)-ithprime(k)), k=1..n): seq(a(n), n=1..70);

MATHEMATICA

an = Table[(PrimePi[n + 1] - PrimePi[n])*(Prime[n + 1] - Prime[n]), {n, 1, 200}] a[0] = 0; a[n_] := a[n] = a[n - 1] + an[[n]] aa = Table[a[n], {n, 0, Length[an]}]

CROSSREFS

Cf. A001223, A010051.

Partial sums of A109578.

Sequence in context: A241274 A088147 A302446 * A109580 A168269 A326936

Adjacent sequences:  A109576 A109577 A109578 * A109580 A109581 A109582

KEYWORD

nonn

AUTHOR

Roger L. Bagula, Jun 29 2005

STATUS

approved

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Last modified July 25 16:39 EDT 2021. Contains 346291 sequences. (Running on oeis4.)