A329539 Numbers m such that the sum of the first m primes as well as the sum of the squares and the sum of the cubes of the first m primes are all prime.

3618, 5840, 7716, 17502, 19460, 22398, 23520, 26852, 33824, 41202, 45848, 47328, 62138, 72950, 82722, 101084, 118062, 127160, 128784, 134012, 136380, 148940, 165240, 173658, 175220, 175310, 177516, 187556, 193692, 203310, 230802, 234032, 279102, 281754, 285518, 289970, 295196, 298652

Offset

1,1

Links

Table of n, a(n) for n=1..38.

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

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

Mathematica

Module[{nn=300000, prs, m1, m2, m3}, prs=Prime[Range[nn]]; m1=Accumulate[ prs]; m2 = Accumulate[prs^2]; m3=Accumulate[prs^3]; Position[Thread[ {m1, m2, m3}], _? (Total[ Boole[ PrimeQ[#]]]==3&)]]//Flatten (* Harvey P. Dale, Jul 28 2021 *)

Prog

(PARI) s=0; t=0; u=0; n=0; forprime(p=2, 1e6, s+=p; t+=p^2; u+=p^3; n++; if(isprime(u) && isprime(t) && isprime(s), print1(n, ", ")))

Crossrefs

Cf. A013916, A098561, A124225.

Sequence in context: A185495 A029829 A187745 * A329540 A223414 A046835

Adjacent sequences: A329536 A329537 A329538 * A329540 A329541 A329542

Keyword

nonn

Author

Michel Marcus, Nov 16 2019

Extensions

Name (description) modified by Harvey P. Dale, Jul 28 2021

Status

approved