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

Author

Odimar Fabeny, Jul 19 2010

Keywords

• nonn
• easy

Comments

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

Examples

			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.
		

Links

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

Programs

Magma

[3*Binomial(NthPrime(n), 2): n in [1..40]]; // Vincenzo Librandi, Feb 13 2015

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 *)

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

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

Extensions

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