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Numbers k such that the sum of the first k*(k+1) primes is prime.
3

%I #11 Dec 08 2018 11:40:15

%S 1,2,3,11,18,31,34,49,57,76,79,84,97,118,139,140,172,175,183,184,185,

%T 191,208,218,221,232,233,247,262,266,294,313,315,323,333,334,339,344,

%U 351,361,366,372,407,413,436,445,461,473,478,500,545,546,556,564,577

%N Numbers k such that the sum of the first k*(k+1) primes is prime.

%H Ray Chandler, <a href="/A322422/b322422.txt">Table of n, a(n) for n = 1..1000</a>

%F A322421(n) = A322420(a(n)) = A007504(A002378(a(n))).

%t f[n_] := Sum[Prime[k], {k, n}]; Select[Range[500],

%t PrimeQ[f[#*(# + 1)]] &]

%Y Cf. A002378, A007504, A322420, A322421.

%K nonn

%O 1,2

%A _Ray Chandler_, Dec 07 2018