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 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. 1
 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 (list; graph; refs; listen; history; text; internal format)
 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

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Last modified July 23 21:46 EDT 2024. Contains 374575 sequences. (Running on oeis4.)