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Sum of piles of first n primes: a(n) = Sum(prime(i)*(2*i-1): 1<=i<=n).
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%I #14 Jan 22 2022 09:39:28

%S 2,11,36,85,184,327,548,833,1224,1775,2426,3277,4302,5463,6826,8469,

%T 10416,12551,15030,17799,20792,24189,27924,32107,36860,42011,47470,

%U 53355,59568,66235,73982,82235,91140,100453,110734,121455,132916,145141,158000,171667,186166,201189,217424,234215,251748

%N Sum of piles of first n primes: a(n) = Sum(prime(i)*(2*i-1): 1<=i<=n).

%H Seiichi Manyama, <a href="/A316322/b316322.txt">Table of n, a(n) for n = 1..10000</a>

%e ............................................ 7

%e ........................... 5 ............ 7 5 7

%e ............ 3 .......... 5 3 5 ........ 7 5 3 5 7

%e 2 ........ 3 2 3 ...... 5 3 2 3 5 .... 7 5 3 2 3 5 7

%e a(1)=2 ... a(2)=11 .... a(3)=36 ...... a(4)=85.

%t nxt[{n_, a_}] := {n + 1, a + Prime[n + 1] (2 n + 1)}; NestList[nxt,{1,2},50][[All,2]] (* _Harvey P. Dale_, Jul 05 2018 *)

%o (PARI) a(n) = sum(i=1, n, prime(i)*(2*i-1)); \\ _Michel Marcus_, Jan 22 2022

%Y Cf. A083215.

%K nonn

%O 1,1

%A _N. J. A. Sloane_, Jul 03 2018, based on _Reinhard Zumkeller_'s A083215.