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A388066
Numbers k such that the sum of the first k primes minus one is prime.
2
17, 33, 43, 45, 55, 57, 59, 63, 71, 103, 115, 117, 121, 123, 129, 133, 139, 153, 155, 159, 181, 187, 189, 193, 211, 213, 273, 275, 283, 291, 305, 331, 335, 341, 347, 351, 365, 367, 373, 395, 405, 413, 441, 445, 473, 495, 513, 535, 541, 543, 619, 655, 673, 689, 699, 701
OFFSET
1,1
COMMENTS
All terms are odd.
LINKS
FORMULA
{k | A007504(k) - 1 is prime}. - Michael S. Branicky, Sep 14 2025
EXAMPLE
17 is a term because prime(1) + ... + prime(17) - 1 = 440 - 1 = 439 and 439 is prime.
MAPLE
s:= proc(n) option remember; `if`(n=0, -1, s(n-1)+ithprime(n)) end:
q:= n-> isprime(s(n)):
select(q, [$1..800])[]; # Alois P. Heinz, Sep 14 2025
MATHEMATICA
Position[Accumulate[Prime[Range[1000]]] - 1, _?PrimeQ] // Flatten (* Amiram Eldar, Sep 15 2025 *)
PROG
(PARI) isok(k) = isprime(vecsum(primes(k))-1);
(PARI) a388066(nterms=50, addend=-1) = {my(s=addend, m=n=0); forprime(p=2, , s+=p; n++; if(isprime(s), print1(n, ", "); if(m++>=nterms, break)))}; \\ Hugo Pfoertner, Sep 15 2025
(Python)
from sympy import sieve, isprime
print([k for k in range(1, 702, 2) if isprime(sum(sieve[1:k+1])-1)])
CROSSREFS
KEYWORD
nonn,easy
AUTHOR
Karl-Heinz Hofmann, Sep 14 2025
STATUS
approved