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a(n) = Sum_{k=1..n} prime(k+1)^prime(k).
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%I #21 Sep 08 2022 08:46:15

%S 9,134,16941,19504112,1792179898149,9906370212804086,

%T 5480396764155014990025,74620951324354865576898512,

%U 4316720792370367095095683949638501,17761887757410618772194137156551786713472772,4113915065494528452775640793448453170290434881585

%N a(n) = Sum_{k=1..n} prime(k+1)^prime(k).

%C Partial sums of A078422. - _Michel Marcus_, Jan 26 2016

%e a(3) = 3^2+5^3+7^5 = 16941.

%t Table[Sum[Prime[k+1]^Prime[k], {k, 1, n}], {n, 1, 12}] (* _Vaclav Kotesovec_, Jan 25 2016 *)

%o (Sage) [sum(nth_prime(i+1)^nth_prime(i) for i in [1..n]) for n in [1..15]] # _Tom Edgar_, Jan 25 2016

%o (Magma) [&+[NthPrime(k+1)^NthPrime(k): k in [1..n]]: n in [1..12]]; // _Vincenzo Librandi_, Jan 26 2016

%o (PARI) a(n) = sum(k=1, n, prime(k+1)^prime(k)); \\ _Michel Marcus_, Jan 26 2016

%Y Cf. A051674, A074745, A078422, A138323.

%K nonn,easy

%O 1,1

%A _Emre APARI_, Jan 25 2016