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%I #26 Sep 08 2022 08:45:28
%S 2,158,192,216,356,426,548,680,1178,1196,1466,1500,1524,2324,2438,
%T 2904,2990,3060,3146,3618,3902,4110,4134,4346,4602,5790,5840,6186,
%U 6344,6710,6720,6836,6990,7592,7632,7716,7790,7838,8156,8420,8622,8658,8664,9092
%N Numbers n such that the sum of the first n primes is prime and the sum of the squares of the first n primes is also prime.
%H Charles R Greathouse IV, <a href="/A124225/b124225.txt">Table of n, a(n) for n = 1..10000</a>
%H G. L. Honaker, Jr. and Chris Caldwell, <a href="https://primes.utm.edu/curios/page.php?short=3618">Prime Curios! 3618</a>
%H Carlos Rivera, <a href="https://www.primepuzzles.net/puzzles/puzz_978.htm">Puzzle 978. Improve this curio</a>, Prime Puzzles and Problems Connection.
%t With[{nn=9100},Position[Thread[{Accumulate[Prime[Range[nn]]],Accumulate[ Prime[ Range[ nn]]^2]}],_?(PrimeQ[ #[[1]]]&&PrimeQ[#[[2]]]&),1,Heads-> False]]//Flatten (* _Harvey P. Dale_, Aug 18 2020 *)
%o (Magma) a013916:=func<n|IsPrime(&+[NthPrime(k): k in [1..n]])>; a098561:=func<n|IsPrime(&+[NthPrime(k)^2: k in [1..n]])>; [n: n in [1..10000]|a013916(n) and a098561(n)]; // _Bruno Berselli_, Dec 28 2011
%o (PARI) s=0;t=0;n=0;forprime(p=2,1e6,s+=p;t+=p^2;n++;if(isprime(t)&&isprime(s),print1(n", "))) \\ _Charles R Greathouse IV_, Dec 28 2011
%Y Intersection of A098561 (Numbers n such that the sum of the squares of the first n primes is prime) and A013916 (Numbers n such that the sum of the first n primes is prime).
%K nonn
%O 1,1
%A _Tanya Khovanova_, Dec 13 2006
%E More terms from _Bruno Berselli_, Dec 28 2011
%E Definition rephrased by _Harvey P. Dale_, Aug 18 2020
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