A124225 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.

2, 158, 192, 216, 356, 426, 548, 680, 1178, 1196, 1466, 1500, 1524, 2324, 2438, 2904, 2990, 3060, 3146, 3618, 3902, 4110, 4134, 4346, 4602, 5790, 5840, 6186, 6344, 6710, 6720, 6836, 6990, 7592, 7632, 7716, 7790, 7838, 8156, 8420, 8622, 8658, 8664, 9092

Offset

1,1

Links

Charles R Greathouse IV, Table of n, a(n) for n = 1..10000

G. L. Honaker, Jr. and Chris Caldwell, Prime Curios! 3618

Carlos Rivera, Puzzle 978. Improve this curio, Prime Puzzles and Problems Connection.

Mathematica

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 *)

Prog

(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
(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

Crossrefs

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).

Sequence in context: A142006 A233575 A233263 * A159030 A064071 A116638

Adjacent sequences: A124222 A124223 A124224 * A124226 A124227 A124228

Keyword

nonn

Author

Tanya Khovanova, Dec 13 2006

Extensions

More terms from Bruno Berselli, Dec 28 2011

Definition rephrased by Harvey P. Dale, Aug 18 2020

Status

approved