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A321342 Numbers k such that if j is the sum of the first k primes, then the sum of the first j primes is prime. 3
1, 9, 15, 19, 73, 85, 87, 103, 121, 157, 175, 277, 313, 317, 341, 357, 375, 385, 391, 421, 443, 447, 523, 525, 539, 571, 607, 611, 645, 701, 779, 783, 791, 799, 823, 831, 835, 853, 889, 907, 911, 925, 977, 1051, 1075, 1081, 1087, 1095, 1117, 1125, 1135, 1157, 1181, 1187, 1223, 1257, 1305, 1325 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,2

COMMENTS

k is in the sequence if A007504(j) is prime, where j = A007504(k). A007504(j) must be odd to be prime, so j must be even and k must be odd. Therefore all terms are odd. The subsequence of primes is A321343.

LINKS

Ray Chandler, Table of n, a(n) for n = 1..16000

Daniel Suteu, Perl program

EXAMPLE

A007504(1) = 2 and A007504(2) = 5, a prime therefore 1 is a term.

A007504(3) = 10 and A007504(10) = 129, not prime, therefore 3 is not a term.

A007504(9) = 100 and A007504(100) = 24133, a prime so 9 is a term.

MAPLE

N:=2000:

for n from 1 to N by 2 do

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

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

if isprime(Y) then print(n);

end if:

end do:

MATHEMATICA

primeSum[n_] := Sum[Prime[i], {i, n}]; Select[Range[300], PrimeQ[primeSum[primeSum[#]]] &] (* Amiram Eldar, Nov 07 2018 *)

PROG

(PARI) sfp(n) = sum(k=1, n, prime(k)); \\ A007504

isok(n) = isprime(sfp(sfp(n))); \\ Michel Marcus, Nov 08 2018

CROSSREFS

Cf. A007504, A013916, A321343.

Sequence in context: A161163 A058211 A038599 * A255763 A079364 A160666

Adjacent sequences:  A321339 A321340 A321341 * A321343 A321344 A321345

KEYWORD

nonn

AUTHOR

David James Sycamore, Nov 06 2018

STATUS

approved

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Last modified October 15 20:04 EDT 2019. Contains 328037 sequences. (Running on oeis4.)