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%I #4 Jul 15 2023 16:47:54
%S 1,2,3,6,10,23,31,46,55,58,66,70,82,91,118,131,151,163,182,187,198,
%T 199,203,222,275,279,334,346,351,358,402,411,462,470,515,582,591,619,
%U 639,650,667,671,679,706,739,750,767,835,851,875,882,899,919,926,962,966
%N Numbers n such that A014148[n] is a prime.
%C Corresponding primes are listed in A122382[n] = A014148[ a(n) ] = {2,7,17,103,467,6577,17189,61627,109919,130531,198109,239579,399557,559313,...}.
%F A014148[n] = Sum[ Sum[ Prime[k], {k,1,m} ], {m,1,n} ]. A014148[ a(n) ] = A122382[n].
%e A014148[n] begins {2,7,17,34,62,103,161,238,338,467,627,824,1062,1343,...}.
%e a(1) = 1 because A014148[1] = 2 is prime.
%e a(2) = 2 because A014148[2] = 7 is prime.
%t p=0;s=0;f=0;Do[p=Prime[n];s=s+p;f=f+s;If[PrimeQ[f],Print[{n,f}]],{n,1,2000}]
%t Position[Nest[Accumulate,Prime[Range[1000]],2],_?PrimeQ]//Flatten (* _Harvey P. Dale_, Jul 15 2023 *)
%Y Cf. A014148, A122382.
%K nonn
%O 1,2
%A _Alexander Adamchuk_, Aug 30 2006
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