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
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
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Magma
[3*Binomial(NthPrime(n), 2): n in [1..40]]; // Vincenzo Librandi, Feb 13 2015
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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
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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
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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(p+1 .. 2p-1) = 3p(p-1)/2 where p is the n-th prime. (End)
Extensions
More terms from Carl R. White and Odimar Fabeny, Jul 27 2010
Comments