|
%I #40 Nov 02 2023 11:11:52
%S 2,7,15,27,45,69,99,135,177,229,289,357,435,519,609,709,821,941,1069,
%T 1207,1351,1503,1665,1837,2023,2221,2425,2635,2851,3073,3313,3571,
%U 3839,4115,4403,4703,5011,5331,5661,6001,6353,6713,7085,7469,7859,8255,8665
%N Sum of n-th row of triangle of primes: 2; 2 3 2; 2 3 5 3 2; 2 3 5 7 5 3 2; ...; where n-th row contains 2n+1 terms.
%C Row sums of A138143. - _Omar E. Pol_, Feb 13 2014
%C For n = 3..9, a(n) = 3*(n^2 - 3*n + 5). - _Nicholas Drozd_, Apr 10 2021
%H Paolo Xausa, <a href="/A061802/b061802.txt">Table of n, a(n) for n = 0..10000</a> (terms 0..1000 from Harry J. Smith)
%F a(n) = a(n-1) + prime(n) + prime(n-1).
%F a(n) = A007504(n) + A007504(n+1) so we have the asymptotic expansion a(n) ~ n^2*log(n). - _Henry Bottomley_, May 30 2001
%t Accumulate[Join[{2},ListConvolve[{1,1},Prime[Range[100]]]]] (* _Paolo Xausa_, Oct 31 2023 *)
%o (PARI) { n=-1; a=q=0; forprime (p=2, prime(1001), write("b061802.txt", n++, " ", a+=p + q); q=p ) } \\ _Harry J. Smith_, Jul 28 2009
%Y Cf. A001043 (first differences), A007504, A138143.
%Y Partial sums of A011974.
%K nonn,easy
%O 0,1
%A _Amarnath Murthy_, May 28 2001
%E More terms from Larry Reeves (larryr(AT)acm.org), May 29 2001
|
