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A321439 Numbers k such that if j is the sum of the first prime(k) primes then the sum of the first j primes is prime. 2
8, 21, 27, 37, 59, 65, 66, 82, 86, 99, 105, 111, 126, 143, 147, 155, 156, 165, 177, 181, 187, 194, 195, 200, 230, 231, 242, 262, 284, 374, 430, 449, 460, 477, 502, 512, 539, 540, 541, 622, 634, 657, 707, 731, 735, 739, 745, 766, 767, 781, 784, 785, 791, 801 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,1

COMMENTS

k is a term if A007504(A007504(prime(k)) is prime. Terms can be even or odd since A007504(A007504(prime(k)) is odd for any k.

LINKS

Ray Chandler, Table of n, a(n) for n = 1..2500

EXAMPLE

8 is a term because prime(8) = 19, A007504(19) = 568, and A007504(568) = 1086557, which is prime.

2 is not a term since prime(2) = 3, A007504(3) = 10 and A007504(10) = 129, which is not prime.

MAPLE

N:=100:

for n from 1 to N do

X:=add(ithprime(k), k=1..ithprime(n));

Y:=add(ithprime(r), r=1..X);

if isprime(Y)then print(n);

end if:

end do:

MATHEMATICA

primeSum[n_] := Sum[Prime[i], {i, n}]; Select[Range[200], PrimeQ[ primeSum[primeSum[Prime[#]]]] &] (* Amiram Eldar, Nov 09 2018 *)

PROG

(Perl)

use ntheory qw(:all);

for (my ($i, $k) = (1, 1); ; ++$k) {

    if (is_prime sum_primes nth_prime sum_primes nth_prime nth_prime $k) {

        print "a($i) = $k\n"; ++$i;

    }

} # Daniel Suteu, Nov 11 2018

(PARI)

sumprimes(n)={my(p=0, s=0); for(i=1, n, p=nextprime(1+p); s+=p); s}

ok(k)={isprime(sumprimes(sumprimes(prime(k))))}

for(n=1, 100, if(ok(n), print1(n, ", "))) \\ Andrew Howroyd, Nov 11 2018

CROSSREFS

Cf. A007504, A013916, A321342, A321343.

Sequence in context: A182602 A123255 A053750 * A271921 A003249 A134862

Adjacent sequences:  A321436 A321437 A321438 * A321440 A321441 A321442

KEYWORD

nonn

AUTHOR

David James Sycamore, Nov 09 2018

EXTENSIONS

a(30)-a(54) from Daniel Suteu, Nov 11 2018

STATUS

approved

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Last modified July 29 23:58 EDT 2021. Contains 346346 sequences. (Running on oeis4.)