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A179545
The sum of the elements within a jump in a Sieve of Eratosthenes table.
12
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
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
KEYWORD
nonn,easy
AUTHOR
Odimar Fabeny, Jul 19 2010
EXTENSIONS
More terms from Carl R. White and Odimar Fabeny, Jul 27 2010
STATUS
approved