A179545 The sum of the elements within a jump in a Sieve of Eratosthenes table.

3, 9, 30, 63, 165, 234, 408, 513, 759, 1218, 1395, 1998, 2460, 2709, 3243, 4134, 5133, 5490, 6633, 7455, 7884, 9243, 10209, 11748, 13968, 15150, 15759, 17013, 17658, 18984, 24003, 25545, 27948, 28773, 33078, 33975, 36738, 39609, 41583, 44634

Offset

1,1

Comments

Every term in this sequence is a multiple of 3. - Nathaniel Johnston, May 04 2011

Links

Nathaniel Johnston, Table of n, a(n) for n = 1..10000

Formula

From Carl R. White, Jul 27 2010: (Start)

a(n) = sum(A000040(n)+1 .. 2*A000040(n)-1) = 3*A000040(n)*(A000040(n)-1)/2.

a(n) = sum(p+1 .. 2p-1) = 3p(p-1)/2 where p is the n-th prime. (End)

a(n) = A179628(n)+A108313(n+1). - R. J. Mathar, Oct 03 2010

Example

2 (3) = 3 (jumps 3), 3 (4,5) = 9 (jumps 4 and 5), 5 (6,7,8,9) = 30 (jumps 6 through 9), 7 (8,... 13) = 63 (jumps 8 through 13), and so on.

Maple

A179545 := proc(n)local k: k:=ithprime(n+1): return 3*k*(k-1)/2: end:
seq(A179545(n), n=0..39); # Nathaniel Johnston, Apr 2011

Mathematica

Table[3 Binomial[Prime[n], 2], {n, 1, 60}] (* Vincenzo Librandi, Feb 13 2015 *)

Prog

(PARI) a(n)=3*binomial(prime(n), 2) \\ Charles R Greathouse IV, May 19 2011
(PARI) apply(n->3*n*(n-1)/2, primes(1000)) \\ Charles R Greathouse IV, May 19 2011
(Magma) [3*Binomial(NthPrime(n), 2): n in [1..40]]; // Vincenzo Librandi, Feb 13 2015

Crossrefs

Sequence in context: A151451 A138938 A154147 * A163129 A074003 A344266

Adjacent sequences: A179542 A179543 A179544 * A179546 A179547 A179548

Keyword

nonn,easy

Author

Odimar Fabeny, Jul 19 2010

Extensions

More terms from Carl R. White and Odimar Fabeny, Jul 27 2010

Status

approved