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%I #31 Sep 08 2022 08:45:54
%S 3,9,30,63,165,234,408,513,759,1218,1395,1998,2460,2709,3243,4134,
%T 5133,5490,6633,7455,7884,9243,10209,11748,13968,15150,15759,17013,
%U 17658,18984,24003,25545,27948,28773,33078,33975,36738,39609,41583,44634
%N The sum of the elements within a jump in a Sieve of Eratosthenes table.
%C Every term in this sequence is a multiple of 3. - _Nathaniel Johnston_, May 04 2011
%H Nathaniel Johnston, <a href="/A179545/b179545.txt">Table of n, a(n) for n = 1..10000</a>
%F From _Carl R. White_, Jul 27 2010: (Start)
%F a(n) = sum(A000040(n)+1 .. 2*A000040(n)-1) = 3*A000040(n)*(A000040(n)-1)/2.
%F a(n) = sum(p+1 .. 2p-1) = 3p(p-1)/2 where p is the n-th prime. (End)
%F a(n) = A179628(n)+A108313(n+1). - _R. J. Mathar_, Oct 03 2010
%e 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.
%p A179545 := proc(n)local k: k:=ithprime(n+1): return 3*k*(k-1)/2: end:
%p seq(A179545(n),n=0..39); # _Nathaniel Johnston_, Apr 2011
%t Table[3 Binomial[Prime[n], 2], {n, 1, 60}] (* _Vincenzo Librandi_, Feb 13 2015 *)
%o (PARI) a(n)=3*binomial(prime(n),2) \\ _Charles R Greathouse IV_, May 19 2011
%o (PARI) apply(n->3*n*(n-1)/2,primes(1000)) \\ _Charles R Greathouse IV_, May 19 2011
%o (Magma) [3*Binomial(NthPrime(n), 2): n in [1..40]]; // _Vincenzo Librandi_, Feb 13 2015
%K nonn,easy
%O 1,1
%A _Odimar Fabeny_, Jul 19 2010
%E More terms from _Carl R. White_ and _Odimar Fabeny_, Jul 27 2010
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